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The paper analyzes the notion of an unbeatable strategy as a game-theoretic solution concept. A general framework (games with relative preferences) suitable for the analysis of this concept is proposed. Basic properties of unbeatable strategies are presented and a number of examples and applications considered. [ABSTRACT FROM AUTHOR]

We consider dominant strategy implementation in a large population aggregative game. The model has strategic complementarities which generates multiple Nash equilibria. Moreover, externalities are positive due to which, all equilibria are socially inefficient. The planner, therefore, constructs a direct mechanism and assigns efficient strategies and transfer levels to agents. Truthful revelation then becomes strictly dominant, which implements efficiency. In our new evolutionary approach to this mechanism, the reported type distribution evolves under dynamics satisfying monotone percentage growth. Such dynamics eliminate dominated strategies thereby ensuring convergence to truthful revelation by all agents. Dominant strategy implementation is, therefore, robust under such evolutionary dynamics. Our evolutionary approach differs from existing models of evolutionary implementation based on potential games. That approach may fail to implement efficiency under strategic complementarities as a Pareto inferior Nash equilibrium can remain asymptotically stable under evolutionary dynamics. Our evolutionary approach is effective even under such strategic complementarities. [ABSTRACT FROM AUTHOR]

Epistemic justifications of solution concepts often refer to type structures that are sufficiently rich. One important notion of richness is that of a complete type structure, i.e., a type structure that induces all possible beliefs about types. For instance, it is often said that, in a complete type structure, the set of strategies consistent with rationality and common belief of rationality are the set of strategies that survive iterated dominance. This paper shows that this classic result is false, absent certain topological conditions on the type structure. In particular, it provides an example of a finite game and a complete type structure in which there is no state consistent with rationality and common belief of rationality. This arises because the complete type structure does not induce all hierarchies of beliefs—despite inducing all beliefs about types. This raises the question: Which beliefs does a complete type structure induce? We provide several positive results that speak to that question. However, we also show that, within ZFC, one cannot show that a complete structure induces all second-order beliefs. [ABSTRACT FROM AUTHOR]

This paper extends Selten's (Int J Game Theory 4:25–55, 1975) notion of perfection to normal-form games of incomplete information and provides conditions on the primitives of a game that ensure the existence of a perfect Bayes–Nash equilibrium. The existence results, which allow for arbitrary (compact, metric) type and/or action spaces and payoff discontinuities, are illustrated in the context of all-pay auctions and Cournot games with incomplete information and cost discontinuities. [ABSTRACT FROM AUTHOR]

I define Weak Implementation under incomplete information. A social choice set is weakly implementable if the set of equilibrium outcomes of some mechanism is a non-empty subset of the social choice set. Weak implementation is a more natural objective than either full or partial implementation in many cases. I show that there are social choice sets where every subset can be weakly implemented, yet the set cannot be fully implemented. I give a complete characterization of the weakly implementable social choice sets under a weak restriction on preferences. As a corollary, I show that in independent private values environments the set of interim efficient social choice functions is weakly implementable whenever it is partially implementable. [ABSTRACT FROM AUTHOR]

Inductive game theory was developed to study the emergence of the subjective views of various individuals in a recurrent social situation. In this paper, we develop a constructive approach for obtaining an inductively derived view (i.d.view). More specifically, we consider two methods: one is a benchmark general case, and the other is a special case taking causality in memories more explicitly into account. The first method is shown to capture the full set of i.d.views in the sense of Kaneko and Kline (Econ Theory 53(1):27–59, 2013). The second method allows us to focus on a finite set of natural candidate i.d.views. We argue that these methods facilitate future work on bounded rationality in interactive settings. [ABSTRACT FROM AUTHOR]

We study the existence and computation of equilibrium in large games with strategic complementarities. Using monotone operators defined on the space of distributions partially ordered with respect to the first-order stochastic dominance, we prove existence of a greatest and least distributional Nash equilibrium. In particular, we obtain our results under a different set of conditions than those in the existing literature. Moreover, we provide computable monotone distributional equilibrium comparative statics with respect to the parameters of the game. Finally, we apply our results to models of social distance, large stopping games, keeping up with the Joneses, as well as a general class of linear non-atomic games. [ABSTRACT FROM AUTHOR]

Many questions of interest in economics can be stated in terms of monotone comparative statics: If a parameter of a constrained optimization problem increases, when does its solution increase as well. We characterize monotone comparative statics in different directions in finite-dimensional Euclidean space by extending the monotonicity theorem of Milgrom and Shannon (Econometrica 62(1):157-180, 1994) to constraint sets ordered in Quah (Econometrica 75(2):401-431, 2007)’s set order. Our characterizations are ordinal and retain the same flavor as their counterparts in the standard theory, showing new connections to the standard theory and presenting new results. The results are highlighted with several applications (in consumer theory, producer theory, and game theory) which were previously outside the scope of the standard theory of monotone comparative statics. [ABSTRACT FROM AUTHOR]

We characterize the properties of convexity, compactness and preservation of upper hemicontinuity for conditional expectation of correspondences via the condition of “nowhere equivalence,” and hence extend the classical results on integration of correspondences. To illustrate the economic applications of those properties, we present new results on large games, abstract economies with asymmetric information and stochastic games. [ABSTRACT FROM AUTHOR]

A fundamental property of choice functions is stability, which, loosely speaking, prescribes that choice sets are invariant under adding and removing unchosen alternatives. We provide several structural insights that improve our understanding of stable choice functions. In particular, (1) we show that every stable choice function is generated by a unique simple choice function, which never excludes more than one alternative, (2) we completely characterize which simple choice functions give rise to stable choice functions, and (3) we prove a strong relationship between stability and a new property of tournament solutions called local reversal symmetry. Based on these findings, we provide the first concrete tournament—consisting of 24 alternatives—in which the tournament equilibrium set fails to be stable. Furthermore, we prove that there is no more discriminating stable tournament solution than the bipartisan set and that the bipartisan set is the unique most discriminating tournament solution which satisfies standard properties proposed in the literature. [ABSTRACT FROM AUTHOR]

This paper considers populations of agents whose behavior when playing some underlying game is governed by perturbed best (or better) response dynamics with perturbation probabilities that depend log-linearly on payoffs, a class that includes the logit choice rule. A convention is a state at which every agent plays a strategy that corresponds to the same strict Nash equilibrium of the underlying game. For coordination games with zero payoff off-diagonal, it is shown that the difficulty of leaving the basin of attraction of a convention can be well approximated by only considering paths of transitions on which an identical perturbation repeatedly affects one of the populations. [ABSTRACT FROM AUTHOR]

We study the impact of switching costs on the long-run outcome in $$2\times 2$$ coordination games played in the circular city model of local interactions. For low levels of switching costs, the predictions are in line with the previous literature and the risk-dominant convention is the unique long-run equilibrium. For intermediate levels of switching costs, the set of long-run equilibria still contain the risk-dominant convention but may also contain conventions that are not risk dominant. The set of long-run equilibria may further be non-monotonic in the level of switching costs, i.e., as switching costs increase the prediction that the risk-dominant convention is the unique long-run equilibrium and the prediction that both conventions are long-run equilibria alternate. Finally, for high levels of switching costs, also non-monomorphic states will be included in the set of long-run equilibria. [ABSTRACT FROM AUTHOR]

Consider a mechanism design setting in which agents acquire costly information about an unknown, payoff-relevant state of nature before participating in the mechanism. Information gathering is covert. We investigate conditions under which (i) efficient implementation and (ii) full surplus extraction are Bayesian incentive compatible and interim individually rational. [ABSTRACT FROM AUTHOR]

We study games of incomplete information and argue that it is important to correctly specify the 'context' within which hierarchies of beliefs lie. We consider a situation where the players understand more than the analyst: It is transparent to the players-but not to the analyst-that certain hierarchies of beliefs are precluded. In particular, the players' type structure can be viewed as a strict subset of the analyst's type structure. How does this affect a Bayesian equilibrium analysis? One natural conjecture is that this doesn't change the analysis-i.e., every equilibrium of the players' type structure can be associated with an equilibrium of the analyst's type structure. We show that this conjecture is wrong. Bayesian equilibrium may fail an Extension Property. This can occur even in the case where the game is finite and the analyst uses the so-called universal structure (to analyze the game)-and, even, if the associated Bayesian game has an equilibrium. We go on to explore specific situations in which the Extension Property is satisfied. [ABSTRACT FROM AUTHOR]

What is the minimal structure that is needed to perform equilibrium analysis in large extensive form games? To answer this question, this paper provides conditions that are simultaneously necessary and sufficient for the existence of a subgame perfect equilibrium in any well-behaved perfect information game defined on a large game tree. In particular, the set of plays needs to be endowed with a topology satisfying two conditions. (a) Nodes are closed as sets of plays; and (b) the immediate predecessor function is an open map. [ABSTRACT FROM AUTHOR]

We provide a new proof of the nonemptiness of approximate cores of games with many players of a finite number of types. Earlier papers in the literature proceed by showing that, for games with many players, equal-treatment cores of their 'balanced cover games,' which are nonempty, can be approximated by equal-treatment $$\varepsilon $$ -cores of the games themselves. Our proof is novel in that we develop a limiting payoff possibilities set and rely on a fixed point theorem. [ABSTRACT FROM AUTHOR]

To prove their Walrasian equilibrium existence theorem, Arrow and Debreu (Econometrica 22(3):265-290, 1954) devised an abstract economy that Shapley and Shubik (J Polit Econ 85:937-968, 1977) criticized as a market game because, especially with untrustworthy traders, it fails to determine a credible outcome away from equilibrium. All this earlier work also postulated a Walrasian auctioneer with complete information about traders' preferences and endowments. To ensure credible outcomes, even in disequilibrium, warehousing is introduced into a multistage market game. To achieve Walrasian outcomes in a large economy with incomplete information, even about traders' endowments, a strategyproof demand revelation mechanism is considered and then extended to include warehousing. [ABSTRACT FROM AUTHOR]

This paper is aimed at widening the scope of applications of majorized correspondences. A new class of majorized correspondences-domain $${\mathcal {U}}$$ -majorized correspondences-is introduced. For them, a maximal element existence theorem is established. Then, sufficient conditions for the existence of an equilibrium in qualitative games are provided. They are used to show the existence of a pure strategy Nash equilibrium in compact quasiconcave games that are either correspondence secure or correspondence transfer continuous. [ABSTRACT FROM AUTHOR]

We provide conditions guaranteeing the existence of Nash equilibrium in games in which players' preferences can be arbitrary binary relations. Our main result generalizes Reny's (Economic Theory, forthcoming) existence result for games with ordered preferences and He and Yannelis' (Economic Theory, forthcoming) existence result for abstract economies with non-ordered preferences. [ABSTRACT FROM AUTHOR]

Multi-player perfect information games are known to admit a subgame-perfect $$\epsilon $$ -equilibrium, for every $$\epsilon >0$$ , under the condition that every player's payoff function is bounded and continuous on the whole set of plays. In this paper, we address the question on which subsets of plays the condition of payoff continuity can be dropped without losing existence. Our main result is that if payoff continuity only fails on a sigma-discrete set (a countable union of discrete sets) of plays, then a subgame-perfect $$\epsilon $$ -equilibrium, for every $$\epsilon >0$$ , still exists. For a partial converse, given any subset of plays that is not sigma-discrete, we construct a game in which the payoff functions are continuous outside this set but the game admits no subgame-perfect $$\epsilon $$ -equilibrium for small $$\epsilon >0$$ . [ABSTRACT FROM AUTHOR]

We introduce a relaxed Nash equilibrium concept for strategic form games, called quasi-Nash equilibrium, which exists in every diagonally transfer quasi-concave games. The quasi-Nash equilibrium has the property to be stable with respect to perturbations on both payoff functions and mistakes in playing pure strategy profiles. We compare our relaxed equilibrium with the Reny equilibrium (introduced in a recent paper) and give stability properties for the Reny equilibrium. [ABSTRACT FROM AUTHOR]

We introduce the concepts of joint games and compatibility. In a joint game, members of the grand coalition have the option to split and participate in different underlying games, thereby maximizing their total worths. In order to determine whether the grand coalition will remain intact, we introduce the notion of compatibility of these games. A set of games is compatible if the core of the joint game is non-empty. We find a necessary and sufficient condition for compatibility. [ABSTRACT FROM AUTHOR]

We investigate a version of the classic Colonel Blotto game in which individual battlefields may have different values. Two players allocate a fixed discrete budget across battlefields. Each battlefield is won by the player who allocates the most to that battlefield. The player who wins the battlefields with highest total value receives a constant winner payoff, while the other player receives a constant loser payoff. We focus on apex games, in which there is one large and several small battlefields. A player wins if he wins the large and any one small battlefield, or all the small battlefields. For each of the games we study, we compute an equilibrium and we show that certain properties of equilibrium play are the same in any equilibrium. In particular, the expected share of the budget allocated to the large battlefield exceeds its value relative to the total value of all battlefields, and with a high probability (exceeding 90 % in our treatments) resources are spread over more battlefields than are needed to win the game. In a laboratory experiment, we find that strategies that spread resources widely are played frequently, consistent with equilibrium predictions. In the treatment where the asymmetry between battlefields is strongest, we also find that the large battlefield receives on average more than a proportional share of resources. In a control treatment, all battlefields have the same value and our findings are consistent with previous experimental findings on Colonel Blotto games. [ABSTRACT FROM AUTHOR]

Most allocation rules for network games presented in the literature assume that the network structure is fixed. We put explicit emphasis on the construction of networks and examine the dynamic formation of networks whose evolution across time periods is stochastic. Time series of networks are studied that describe processes of network formation where links may appear or disappear at any period. Moreover, convergence to an efficient network is not necessarily prescribed. Transitions from one network to another are random and ruled by a stochastic process, typically a Markov chain. We propose the link-based scenario allocation rule for such dynamic random network formation processes and provide its axiomatic characterization. By considering a monotone game and a particular (natural) network formation process, we recover the link-based flexible network allocation rule of Jackson (Games Econ Behav 51:128-154, ). [ABSTRACT FROM AUTHOR]

The folk theorem for infinitely repeated games with imperfect public monitoring implies that for a general class of games, nearly efficient payoffs can be supported in perfect public equilibrium (PPE), provided the monitoring structure is sufficiently rich and players are arbitrarily patient. This paper shows that for stage games in which actions of players interfere strongly with each other, exactly efficient payoffs can be supported in PPE even when the monitoring structure is not rich and players are not arbitrarily patient. The class of stage games we study abstracts many environments including resource sharing. [ABSTRACT FROM AUTHOR]

A Nash equilibrium $$x$$ of a normal-form game $$G$$ is essential if any perturbation of $$G$$ has an equilibrium close to $$x$$ . Using payoff perturbations, we identify a new collection of games containing a dense, residual subset of games whose Nash equilibria are all essential. This collection covers economic examples that cannot be handled by extant results and subsumes the sets of games considered in the literature. [ABSTRACT FROM AUTHOR]

We study the implications of procedural fairness on the share of income that should be redistributed. We formulate procedural fairness as a particular non-cooperative bargaining game and examine the stationary subgame perfect equilibria of the game. The equilibrium outcome is called tax equilibrium and is shown to be unique. The procedurally fair tax rate is defined as the tax rate that results in the limit of tax equilibria when the probability that negotiations break down converges to zero. The procedurally fair tax rate is shown to be unique. We also provide a characterization of the procedurally fair tax rate that involves the probability mass of below average income citizens and a particular measure of the citizens' boldness. This characterization is then used to show that in a number of interesting cases, the procedurally fair tax rate equals the probability mass of below average income citizens. [ABSTRACT FROM AUTHOR]

We derive a necessary and sufficient condition for the existence of equilibria with only two active players in the all-pay auction with complete information and identity-dependent externalities. This condition shows that the generic equilibrium of the standard all-pay auction is robust to the introduction of 'small' identity-dependent externalities. In general, however, the presence of identity-dependent externalities invalidates well-established qualitative results concerning the set of equilibria of the first-price all-pay auction with complete information. With identity-dependent externalities, equilibria are generally not payoff equivalent, and identical players may earn different payoffs in equilibrium. These observations show that Siegel's (Econometrica 77(1), 71-92, ) results characterizing the set of equilibrium payoffs in all-pay contests, including the all-pay auction as a special case, do not extend to environments with identity-dependent externalities. We further compare the all-pay auction with identity-dependent externalities to the first-price winner-pay auction with identity-dependent externalities. We demonstrate that the equilibrium payoffs of the all-pay auction and the 'undominated strategy equilibrium' payoffs of the winner-pay auction (Funk in Int J Game Theory 25(1), 51-64, ) cannot be ranked unambiguously in the presence of identity-dependent externalities by providing examples of environments where equilibrium payoffs in the all-pay auction dominate those of the undominated strategy equilibria in the winner-pay auction and vice versa. [ABSTRACT FROM AUTHOR]

We study equilibrium in large games of strategic complementarities (GSC) with differential information. We define an appropriate notion of distributional Bayesian Nash equilibrium and prove its existence. Furthermore, we characterize order-theoretic properties of the equilibrium set, provide monotone comparative statics for ordered perturbations of the space of games, and provide explicit algorithms for computing extremal equilibria. We complement the paper with new results on the existence of Bayesian Nash equilibrium in the sense of Balder and Rustichini (J Econ Theory 62(2):385-393, ) or Kim and Yannelis (J Econ Theory 77(2):330-353, ) for large GSC and provide an analogous characterization of the equilibrium set as in the case of distributional Bayesian Nash equilibrium. Finally, we apply our results to riot games, beauty contests, and common value auctions. In all cases, standard existence and comparative statics tools in the theory of supermodular games for finite numbers of agents do not apply in general, and new constructions are required. [ABSTRACT FROM AUTHOR]

The theory of revealed preferences offers an elegant way to test the neoclassical model of utility maximization subject to a linear budget constraint. In many settings, however, the set of available consumption bundles does not take the form of a linear budget set. In this paper, we adjust the theory of revealed preferences to handle situations where the set of feasible bundles is finite. Such situations occur frequently in many real life and experimental settings. We derive the revealed preference conditions for consistency with utility maximization in this finite choice set setting. Interestingly, we find that it is necessary to make a distinction between the cases where the underlying utility function is weakly monotone, strongly monotone and/or concave. Next, we provide conditions on the structure of the finite choice sets for which the usual revealed preference condition (i.e. GARP) is still valid. We illustrate the relevance of our results by means of an illustration based on two experimental data sets that contain choice behaviour from children and young adults. [ABSTRACT FROM AUTHOR]

We introduce a 'nestedness' relation for a general class of sender-receiver games and compare equilibrium properties, in particular the amount of information transmitted, across games that are nested. Roughly, game $$B$$ is nested in game $$A$$ if the players' optimal actions are closer in game $$B$$ . We show that under some conditions, more information is transmitted in the nested game in the sense that the receiver's expected equilibrium payoff is higher. The results generalize the comparative statics and welfare comparisons with respect to preferences in the seminal paper of Crawford and Sobel (Econometrica 50(6):1431-1452, ). We also derive new results with respect to changes in priors in addition to changes in preferences. We illustrate the usefulness of the results in three applications: (i) delegation to an intermediary with a different prior, (ii) the choice between centralization and delegation, and (iii) two-way communication with an informed principal. [ABSTRACT FROM AUTHOR]

In a sequential-move, finitely repeated prisoners' dilemma game (FRPD), cooperation can be sustained if the first-mover believes her opponent might be a behavioral type who plays a tit-for-tat strategy in every period. We test this theory by revealing second-mover histories from an earlier FRPD experiment to their current opponent. Despite eliminating the possibility of reputation-building, aggregate cooperation actually increases when histories are revealed. Cooperative histories lead to increased trust, but negative histories do not cause decreased trust. We develop a behavioral model to explain these findings. [ABSTRACT FROM AUTHOR]

This paper provides assumptions for a limit Folk theorem in stochastic games with finite horizon. In addition to the asymptotic assumptions à la Dutta (J Econ Theory 66:1-32, ) I present an additional assumption under which the Folk theorem holds in stochastic games when the horizon is long but finite. This assumption says that the limit set of SPE payoffs contains a state invariant payoff vector $$w$$ and, for each player $$i$$ , another payoff vector that gives less than $$w$$ to $$i$$ . I present two alternative assumptions, one on a finite truncation of the stochastic game and the other on stage games and on the transition function, that imply this assumption. [ABSTRACT FROM AUTHOR]

This paper studies the existence of pure-strategy Nash equilibria for nonatomic games where players take actions in infinite-dimensional Banach spaces. For any infinite-dimensional Banach space, if the player space is modeled by the Lebesgue unit interval, we construct a nonatomic game which has no pure-strategy Nash equilibrium. But if the player space is modeled by a saturated probability space, there is a pure-strategy Nash equilibrium in every nonatomic game. Finally, if every game with a fixed nonatomic player space and a fixed infinite-dimensional action space has a pure-strategy Nash equilibrium, the underlying player space must be saturated. [ABSTRACT FROM AUTHOR]

In the literature, various models of games with restricted cooperation can be found. In those models, instead of allowing for all subsets of the set of players to form, it is assumed that the set of feasible coalitions is a subset of the power set of the set of players. In this paper, we consider such sets of feasible coalitions that follow from a permission structure on the set of players, in which players need permission to cooperate with other players. We assume the permission structure to be an oriented tree. This means that there is one player at the top of the permission structure, and for every other player, there is a unique directed path from the top player to this player. We introduce a new solution for these games based on the idea of the Average Tree value for cycle-free communication graph games. We provide two axiomatizations for this new value and compare it with the conjunctive permission value. [ABSTRACT FROM AUTHOR]

We characterize the essential stability of games with a continuum of players, where strategy profiles may affect objective functions and admissible strategies. Taking into account the perturbations defined by a continuous mapping from a complete metric space of parameters to the space of continuous games, we prove that essential stability is a generic property and every game has a stable subset of equilibria. These results are extended to discontinuous large generalized games assuming that only payoff functions are subject to perturbations. We apply our results in an electoral game with a continuum of Cournot-Nash equilibria, where the unique essential equilibrium is that only politically engaged players participate in the electoral process. In addition, employing our results for discontinuous games, we determine the stability properties of competitive prices in large economies. [ABSTRACT FROM AUTHOR]

We model constitutions by effectivity functions. We assume that the constitution is common knowledge among the members of the society. However, the preferences of the citizens are private information. We investigate whether there exist decision schemes (i.e., functions that map profiles of (dichotomous) preferences on the set of outcomes to lotteries on the set of social states), with the following properties: (i) The distribution of power induced by the decision scheme is identical to the effectivity function under consideration; and (ii) the (incomplete information) game associated with the decision scheme has a Bayesian Nash equilibrium in pure strategies. If the effectivity function is monotonic and superadditive, then we find a class of decision schemes with the foregoing properties. [ABSTRACT FROM AUTHOR]

This paper examines a global games model of speculative attacks in which speculators can choose to attack any one of a number of targets. In the canonical global games model of speculative attacks with a single target, it is well known that there exists a unique equilibrium that survives iterative deletion of dominated strategies, characterized by the threshold values of the private signal and the fundamentals. This paper shows that with two targets, there is again a unique, dominance-solvable equilibrium. In this equilibrium, the threshold value of signal for attacking a given currency is a function of the signal for the other target, and the threshold value of fundamentals that determines the outcome of attack on one currency is a function of the other target's fundamentals. Under certain condition on the noise distribution, the result is shown to extend to environments with any $$N$$ symmetric targets. This paper then presents a number of numerical examples and shows, among other results, that more accurate private signals have a decoupling effect on the outcomes of attack on different currencies. [ABSTRACT FROM AUTHOR]

We discuss an analytically tractable discrete-time dynamic game in which a finite number of players extract a renewable resource. We characterize a symmetric Markov-perfect Nash equilibrium of this game and derive a necessary and sufficient condition under which the resource does not become extinct in equilibrium. This condition requires that the intrinsic growth rate of the resource exceeds a certain threshold value that depends on the number of players and on their time-preference rates. [ABSTRACT FROM AUTHOR]

We introduce and analyze three definitions of equilibrium for finite extensive games with imperfect information and ambiguity averse players. In a setting where players' preferences are represented by maxmin expected utility, as characterized in Gilboa and Schmeidler (J Math Econ 18(2):141-153, ), our definitions capture the intuition that players may consider the possibility of slight arbitrary mistakes. This generalizes the idea leading to trembling-hand perfect equilibrium as introduced in Selten (Int J Game Theory 4(1):25-55, ), by allowing for ambiguous trembles characterized by sets of distributions. We prove existence for two of our equilibrium notions and relate our definitions to standard equilibrium concepts with expected utility maximizing players. Our analysis shows that ambiguity aversion can lead to behavioral implications that are distinct from those attained under expected utility maximization, even if ambiguous beliefs only arise from the possibility of slight mistakes in the implementation of unambiguous strategies. [ABSTRACT FROM AUTHOR]

This paper characterizes both point-rationalizability and rationalizability in large games when societal responses are formulated as distributions or averages of individual actions. The sets of point-rationalizable and rationalizable societal responses are defined and shown to be convex, compact and equivalent to those outcomes that survive iterative elimination of never best responses, under point-beliefs and probabilistic beliefs, respectively. Given the introspection and mentalizing that rationalizability notions presuppose, one motivation behind the work is to examine their viability in situations where the terms rationality and full information can be given a more parsimonious, and thereby a more analytically viable, expression. [ABSTRACT FROM AUTHOR]

We consider competitive markets with asymmetric information. We define a notion of equilibrium that allows individuals to act strategically both as buyers and as sellers. In an example, the wage is common to all types of labor, and it does not reveal information concerning the skill levels of workers. However, at the solution we propose, an informed firm can take advantage of its superior information: it can choose the extent to which it concentrates its employment offers to workers of different types. The probabilities that offers to workers of different types produce a hire are treated parametrically by firms who have correct expectations about them, and firms forego the wage when they extend an offer whether the offer is successful or not. In a general framework, we prove that equilibria exist. [ABSTRACT FROM AUTHOR]

History-dependent strategies are often used to support cooperation in repeated game models. Using the indefinitely repeated common-pool resource assignment game and a perfect stranger experimental design, this paper reports novel evidence that players who have successfully used an efficiency-enhancing turn taking strategy will teach other players in subsequent supergames to adopt this strategy. We find that subjects engage in turn taking frequently in both the Low Conflict and the High Conflict treatments. Prior experience with turn taking significantly increases turn taking in both treatments. Moreover, successful turn taking often involves fast learning, and individuals with turn taking experience are more likely to be teachers than inexperienced individuals. The comparative statics results show that teaching in such an environment also responds to incentives, since teaching is empirically more frequent in the Low Conflict treatment with higher benefits and lower costs. [ABSTRACT FROM AUTHOR]

The paper fully characterizes the class of Nash implementable social choice correspondences ( SCCs) by mechanisms endowed with Saijo's message space specification- $$s$$- mechanisms. This class of SCCs is equivalent to the class of Nash implementable SCCs, though any game form involving 'one less' preference announcements breaks this equivalence relationship down. [ABSTRACT FROM AUTHOR]

We introduce spaces of discontinuous games in which games having essential Nash equilibria are the generic case. In order to prove the existence of essential Nash equilibria in such spaces, we provide new results on the Ky Fan minimax inequality. In the setting of potential games, we show that games with essential Nash equilibria are the generic case when their potentials satisfy a condition called weak upper pseudocontinuity that is weaker than upper semicontinuity. [ABSTRACT FROM AUTHOR]

We provide a direct proof of the existence of perfect equilibria in finite normal form games and extensive games with perfect recall. It is done by constructing a correspondence whose fixed points are precisely the perfect equilibria of a given finite game. Existence of a fixed point is secured by a generalization of Kakutani theorem, which is proved in this paper. This work offers a new approach to perfect equilibria, which would hopefully facilitate further study on this topic. We also hope our direct proof would be the first step toward building an algorithm to find the set of all perfect equilibria of a strategic game. [ABSTRACT FROM AUTHOR]

Some of the best-known results in mechanism design depend critically on Myerson's (Math Oper Res 6:58-73, ) regularity condition. For example, the second-price auction with reserve price is revenue maximizing only if the type distribution is regular. This paper offers two main findings. First, a new interpretation of regularity is developed-similar to that of a monotone hazard rate-in terms of being the next to fail. Second, using expanded concepts of concavity, a tight sufficient condition is obtained for a density to define a regular distribution. New examples of regular distributions are identified. Applications are discussed. [ABSTRACT FROM AUTHOR]

We study equilibrium existence in normal form games in which it is possible to associate with each nonequilibrium point an open neighborhood, a set of players, and a collection of deviation strategies, such that at any nonequilibrium point of the neighborhood, a player from the set can increase her payoff by switching to the deviation strategy designated for her. An equilibrium existence theorem for compact, quasiconcave games with two players is established as an application of a general equilibrium existence result for qualitative games. A new form of the better-reply security condition, called the strong single deviation property, is proposed. [ABSTRACT FROM AUTHOR]