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The prevailing approaches to modelling interactive uncertainty with epistemic models in economics are state-based and type-based. We explicitly formulate two general procedures that transform state models into type models and vice versa. Both transformation procedures preserve the belief hierarchies as well as the common prior assumption. By means of counterexamples it is shown that the two procedures are not inverse to each other. However, if attention is restricted to maximally reduced epistemic models, then isomorphisms can be constructed and an inverse relationship emerges.

In this paper we explore the absentminded driver problem using two different scenarios. In the first scenario we assume that the driver is capable of reasoning about his degree of absentmindedness before he hits the highway. This leads to a Savage-style model where the states are mutually exclusive and the act-state independence is in place. In the second we employ centred possibilities, by modelling the states (i.e. the events about which the driver is uncertain) as the possible final destinations indexed by a time period. The optimal probability we find for continuing at an exit is different from almost all papers in the literature. In this scenario, act-state independence is still violated, but states are mutually exclusive and the driver arrives at his optimal choice probability via Bayesian updating. We show that our solution is the only one guaranteeing immunity from sure loss via a Dutch strategy, and that – despite initial appearances – it is time consistent. This raises important implications for the rationality of commitment in such scenarios.

We study bargaining models in discrete time with a finite number of players, stochastic selection of the proposing player, endogenously determined sets and orders of responders, and a finite set of feasible alternatives. The standard optimality conditions and system of recursive equations may not be sufficient for the existence of a subgame perfect equilibrium in stationary strategies (SSPE) in case of costless delay. We present a characterization of SSPE that is valid for both costly and costless delay. We address the relationship between an SSPE under costless delay and the limit of SSPEs under vanishing costly delay. An SSPE always exists when delay is costly, but not necessarily so under costless delay, even when mixed strategies are allowed for. This is surprising as a quasi SSPE, a solution to the optimality conditions and the system of recursive equations, always exists. The problem is caused by the potential singularity of the system of recursive equations, which is intimately related to the possibility of perpetual disagreement in the bargaining process.

In a local interaction model agents situated on a circle play bilateral prisoners’ dilemmas with their immediate neighbors and have three possible strategies: cooperate in all interactions (altruistic), defect in all interactions (egoistic), or cooperate with one immediate neighbor with probability 1=2 (partial cooperation). After each period the agents adopt the strategy with the highest average payoff in their observed local neighborhood (naive imitation). The absorbing states of the process are outlined and analysed. There does not exist an absorbing state in which the partially cooperative strategy coexists with any of the other strategies. The partially cooperative strategy limits the diffusion of altruistic behavior in the population. Even though clustering of altruists is generally beneficial for sustaining altruism, relatively big groups of altruists at the onset actually enable the spread of the partially cooperative strategy.

A mechanism allocates one unit of an infinitely divisible commodity among agents reporting a number between zero and one. Nash, Pareto optimal Nash, and strong equilibria are analyzed for the case where the agents have single-dipped preferences. One of the main results is that when the mechanism is anonymous, monotonic, standard, and order preserving, then the Pareto optimal Nash and strong equilibria coincide and assign Pareto optimal allocations that are characterized by so-called maximal coalitions: members of a maximal coalition prefer an equal coalition share over obtaining zero, whereas the outside agents prefer zero over obtaining an equal share from joining the coalition.

A mechanism allocates one unit of an infinitely divisible commodity among agents reporting a number between zero and one. Nash, Pareto optimal Nash, and strong equilibria are analyzed for the case where the agents have single-dipped preferences. One of the main results is that when the mechanism is anonymous, monotonic, standard, and order preserving, then the Pareto optimal Nash and strong equilibria coincide and assign Pareto optimal allocations that are characterized by so-called maximal coalitions: members of a maximal coalition prefer an equal coalition share over obtaining zero, whereas the outside agents prefer zero over obtaining an equal share from joining the coalition.

Betrayal aversion is an important factor in the decision to trust. Trust in members of one’s own social group (ingroup members) is often higher than that in members of other groups (outgroup members). In this paper, I study (i) how betrayal aversion contributes to in-/outgroup discrimination in trust and (ii) how this contribution evolves as social groups solidify.

Betrayal aversion is an important factor in the decision to trust. Trust in members of one’s own social group (ingroup members) is often higher than that in members of other groups (outgroup members). In this paper, I study (i) how betrayal aversion contributes to in-/outgroup discrimination in trust and (ii) how this contribution evolves as social groups solidify.

Betrayal aversion is an important factor in the decision to trust. Trust in members of one’s own social group (ingroup members) is often higher than that in members of other groups (outgroup members). In this paper, I study (i) how betrayal aversion contributes to in-/outgroup discrimination in trust and (ii) how this contribution evolves as social groups solidify.

We review the literature on various approaches to modeling animal intergroup conflict behavior in theoretical biology, highlight the intricacies emerging in the process of adding due biological realism to such models, and point out recent empirical findings that can inspire future theorizing. (c) 2017 Elsevier B.V. All rights reserved.

We review the literature on various approaches to modeling animal intergroup conflict behavior in theoretical biology, highlight the intricacies emerging in the process of adding due biological realism to such models, and point out recent empirical findings that can inspire future theorizing. (c) 2017 Elsevier B.V. All rights reserved.

We introduce the idea that a player believes at every stage of a dynamic game that his opponents will choose rationally in the future and have chosen rationally in a restricted way in the past. This is summarized by the concept of common belief in future and restricted past rationality, which is defined epistemically. Moreover, it is shown that every properly rationalizable strategy of the normal form of a dynamic game can be chosen in the dynamic game under common belief in future and restricted past rationality. We also present an algorithm that uses strict dominance, and show that it selects exactly those strategies that can be chosen under common belief in future and restricted past rationality.

During the COVID-19 pandemic, traditional (offline) chess tournaments were prohibited and instead held online. We exploit this unique setting to assess the impact of remote work policies on the cognitive performance of individuals. Using the artificial intelligence embodied in a powerful chess engine to assess the quality of chess moves and associated errors, we find a statistically and economically significant decrease in performance when an individual competes remotely versus offline in a face-to-face setting. The effect size decreases over time, suggesting an adaptation to the new remote setting.

We propose a solution concept for social environments called social rationalizability with mediation that identifies the consequences of common knowledge of rationality and farsightedness. In a social environment several coalitions may and could be willing to move at the same time. Individuals not only hold conjectures about the behaviors of other individuals but also about how a mediator is going to solve conflicts of interest. The set of socially rationalizable outcomes with mediation is shown to be non-empty for all social environments and it can be computed by an iterative reduction procedure. We show that social rationalizability with mediation does not necessarily satisfy coalitional rationality when the number of coalition members is greater than two.

We propose a solution concept for social environments called social rationalizability with mediation that identifies the consequences of common knowledge of rationality and farsightedness. In a social environment several coalitions may and could be willing to move at the same time. Individuals not only hold conjectures about the behaviors of other individuals but also about how a mediator is going to solve conflicts of interest. The set of socially rationalizable outcomes with mediation is shown to be non-empty for all social environments and it can be computed by an iterative reduction procedure. We show that social rationalizability with mediation does not necessarily satisfy coalitional rationality when the number of coalition members is greater than two.

We propose a solution concept for social environments called social rationalizability with mediation that identifies the consequences of common knowledge of rationality and farsightedness. In a social environment several coalitions may and could be willing to move at the same time. Individuals not only hold conjectures about the behaviors of other individuals but also about how a mediator is going to solve conflicts of interest. The set of socially rationalizable outcomes with mediation is shown to be non-empty for all social environments and it can be computed by an iterative reduction procedure. We show that social rationalizability with mediation does not necessarily satisfy coalitional rationality when the number of coalition members is greater than two.

We consider a matching with contracts model in the presence of liquidity constraints on the buyers side. Liquidity constraints can be either soft or hard. A convergent sequence of economies with increasingly stringent soft liquidity constraints is an economy with hard liquidity constraints at the limit. The limit of a corresponding convergent sequence of competitive equilibria may fail to be a competitive equilibrium in the limit economy. We establish limit results of two alternative notions of competitive equilibrium, quantity-constrained competitive equilibrium and expectational equilibrium, which do not suffer from such discontinuity problems. The implications of these limit results are discussed.

We consider a matching with contracts model in the presence of liquidity constraints on the buyers side. Liquidity constraints can be either soft or hard. A convergent sequence of economies with increasingly stringent soft liquidity constraints is an economy with hard liquidity constraints at the limit. The limit of a corresponding convergent sequence of competitive equilibria may fail to be a competitive equilibrium in the limit economy. We establish limit results of two alternative notions of competitive equilibrium, quantity-constrained competitive equilibrium and expectational equilibrium, which do not suffer from such discontinuity problems. The implications of these limit results are discussed.

We consider a matching with contracts model in the presence of liquidity constraints on the buyers side. Liquidity constraints can be either soft or hard. A convergent sequence of economies with increasingly stringent soft liquidity constraints is an economy with hard liquidity constraints at the limit. The limit of a corresponding convergent sequence of competitive equilibria may fail to be a competitive equilibrium in the limit economy. We establish limit results of two alternative notions of competitive equilibrium, quantity-constrained competitive equilibrium and expectational equilibrium, which do not suffer from such discontinuity problems. The implications of these limit results are discussed.

The solution concept of iterated strict dominance for static games with complete information recursively deletes choices that are inferior. Here, we devise such an algorithm for the more general case of incomplete information. The ensuing solution concept of generalized iterated strict dominance is characterized in terms of common belief in rationality as well as in terms of best response sets. Besides, we provide doxastic conditions that are necessary and sufficient for modelling complete information from a one-person perspective.

This paper studies adaptive learning in the class of weighted network games. This class of games includes applications like research and development within interlinked firms, crime within social networks, the economics of pollution, and defense expenditures within allied nations. We show that for every weighted network game, the set of pure Nash equilibria is non-empty and, generically, finite. Pairs of players are shown to have jointly profitable deviations from interior Nash equilibria. If all interaction weights are either non-negative or non-positive, then Nash equilibria are Pareto inefficient. We show that quite general learning processes converge to a Nash equilibrium of a weighted network game if every player updates with some regularity.

In this paper we introduce a novel framework that allows us to model games with players who reason about the opponents’ rationality only in some part of the game tree. We refer to this type of bounded rationality as limited focus. In particular, players try to rationalize their opponents’ moves only at the histories they focus on, i.e., formally, they strongly believe in their opponents’ rationality in these particular histories only. Our main result characterizes the strategy profiles that can be played under rationality and common strong belief in rationality by means of a simple elimination procedure, for every specification of the players’ focus. Finally, we present several special cases and applications of our framework, and we discuss how it differs from other forms of bounded perception such as unawareness.

We study zero-sum repeated games where the minimizing player has to pay a certain cost each time he changes his action. Our contribution is twofold. First, we show that the value of the game exists in stationary strategies, depending solely on the previous action of the minimizing player, not the entire history. We provide a full characterization of the value and the optimal strategies. The strategies exhibit a robustness property and typically do not change with a small perturbation of the switching costs. Second, we consider a case where the minimizing player is limited to playing simpler strategies that are completely history-independent. Here too, we provide a full characterization of the (minimax) value and the strategies for obtaining it. Moreover, we present several bounds on the loss due to this limitation.

We study zero-sum repeated games where the minimizing player has to pay a certain cost each time he changes his action. Our contribution is twofold. First, we show that the value of the game exists in stationary strategies, depending solely on the previous action of the minimizing player, not the entire history. We provide a full characterization of the value and the optimal strategies. The strategies exhibit a robustness property and typically do not change with a small perturbation of the switching costs. Second, we consider a case where the minimizing player is limited to playing simpler strategies that are completely history-independent. Here too, we provide a full characterization of the (minimax) value and the strategies for obtaining it. Moreover, we present several bounds on the loss due to this limitation.

We propose a solution concept for social environments called social rationalizability with mediation that identifies the consequences of common knowledge of rationality and farsightedness. In a social environment several coalitions may and could be willing to move at the same time. Individuals not only hold conjectures about the behaviors of other individuals but also about how a mediator is going to solve conflicts of interest. The set of socially rationalizable outcomes with mediation is shown to be non-empty for all social environments and it can be computed by an iterative reduction procedure. We show that social rationalizability with mediation does not necessarily satisfy coalitional rationality when the number of coalition members is greater than two.

This paper studies a multiple-receiver Bayesian persuasion model, where a sender communicates with receivers who have homogeneous beliefs and aligned preferences. The sender wants to implement a proposal and commits to a communication strategy which sends private (possibly) correlated messages to the receivers, who are in an exogenous and commonly known network. Receivers can observe their neighbors’ private messages and after updating their beliefs, vote sincerely on the proposal. We examine how networks of shared information affect the sender’s gain from persuasion and find that in many cases it is not restricted by the additional information provided by the receivers’ neighborhoods. Perhaps surprisingly, the sender’s gainfrom persuasion is not monotonically decreasing with the density of the network.

This paper studies a multiple-receiver Bayesian persuasion model, where a sender communicates with receivers who have homogeneous beliefs and aligned preferences. The sender wants to implement a proposal and commits to a communication strategy which sends private (possibly) correlated messages to the receivers, who are in an exogenous and commonly known network. Receivers can observe their neighbors’ private messages and after updating their beliefs, vote sincerely on the proposal. We examine how networks of shared information affect the sender’s gain from persuasion and find that in many cases it is not restricted by the additional information provided by the receivers’ neighborhoods. Perhaps surprisingly, the sender’s gain from persuasion is not monotonically decreasing with the density of the network.

We propose a solution concept for social environments called social rationalizability with mediation that identifies the consequences of common knowledge of rationality and farsightedness. In a social environment several coalitions may and could be willing to move at the same time. Individuals not only hold conjectures about the behaviors of other individuals but also about how a mediator is going to solve conflicts of interest. The set of socially rationalizable outcomes with mediation is shown to be non-empty for all social environments and it can be computed by an iterative reduction procedure. We show that social rationalizability with mediation does not necessarily satisfy coalitional rationality when the number of coalition members is greater than two.

The threat of revolution disciplines the elites, inducing them to strategically share some of their wealth in order to prevent social unrest. This behavioral conjecture is prominently used to explain franchise extension and welfare state expansion. We test this conjecture in a controlled laboratory experiment. We model a society whose members can produce wealth by coordinating conflicting interests. Coordination is facilitated through a status-ranking. Compliance with the ranking yields an efficient yet inequitable payoff distribution. Between treatments, we vary (a) whether overthrows – which reset the status-ranking via collective disobedience – are possible or not, and (b) whether voluntary redistributive transfers – which high-status players can use to appease low-status players – are available or not. In contrast to established thinking, we find that, on average, the threat of being overthrown does not lead to more wealth-sharing as high-status players fail to provide sufficient redistribution to prevent overthrows.

This paper studies a model of network formation in which agents create links following a simple heuristic -- they invest their limited resources proportionally more in neighbours who have fewer links. This decision rule captures the notion that when considering social value more connected agents are on average less beneficial as neighbours and node degree is a useful proxy when payoffs are difficult to compute. The decision rule illustrates an externalities effect whereby an agent's actions also influence his neighbours' neighbours. Besides complete networks and fragmented networks with complete components, the pairwise stable networks produced by this model include many non-standard ones with characteristics observed in real life networks like clustering and irregular components. Multiple stable states can develop from the same initial structure -- the stable networks could have cliques linked by intermediary agents while sometimes they have a core-periphery structure. The observed pairwise stable networks have close to optimal welfare. This limited loss of welfare is due to the fact that when a link is established, this is beneficial to the linking agents, but makes them less attractive as neighbours for others, thereby partially internalising the externalities the new connection has generated.

This paper studies a model of network formation in which agents create links following a simple heuristic -- they invest their limited resources proportionally more in neighbours who have fewer links. This decision rule captures the notion that when considering social value more connected agents are on average less beneficial as neighbours and node degree is a useful proxy when payoffs are difficult to compute. The decision rule illustrates an externalities effect whereby an agent's actions also influence his neighbours' neighbours. Besides complete networks and fragmented networks with complete components, the pairwise stable networks produced by this model include many non-standard ones with characteristics observed in real life networks like clustering and irregular components. Multiple stable states can develop from the same initial structure -- the stable networks could have cliques linked by intermediary agents while sometimes they have a core-periphery structure. The observed pairwise stable networks have close to optimal welfare. This limited loss of welfare is due to the fact that when a link is established, this is beneficial to the linking agents, but makes them less attractive as neighbours for others, thereby partially internalising the externalities the new connection has generated.

This paper experimentally investigates excessive risk taking in contest schemes by implementing a novel stopping task based on Seel and Strack (2013). In this stylized setting, managers with contest payoffs have an incentive to delay halting projects with a negative expectation, with the induced inefficiency being highest for a moderately negative drift. The experiment systematically varies the negative drift (between-subjects) and the payoff incentives (within-subject). We find evidence for excessive risk taking in all our treatment conditions, with the non-monotonicity at least as problematic as predicted. Contrary to the theoretical predictions, this aggregate pattern of behaviour is seen even without contest incentives. Further analysis suggests that many subjects display behaviour consistent with some intrinsic motivation for taking risk. This intrinsic motive and the strategic motive for excessive risk taking reinforce the non-monotonicity. The experiment uncovers a behavioural nuance where contest incentives crowd out an intrinsic inclination to gamble.

This paper experimentally investigates excessive risk taking in contest schemes by implementing a novel stopping task based on Seel and Strack (2013). In this stylized setting, managers with contest payoffs have an incentive to delay halting projects with a negative expectation, with the induced inefficiency being highest for a moderately negative drift. The experiment systematically varies the negative drift (between-subjects) and the payoff incentives (within-subject). We find evidence for excessive risk taking in all our treatment conditions, with the non-monotonicity at least as problematic as predicted. Contrary to the theoretical predictions, this aggregate pattern of behaviour is seen even without contest incentives. Further analysis suggests that many subjects display behaviour consistent with some intrinsic motivation for taking risk. This intrinsic motive and the strategic motive for excessive risk taking reinforce the non-monotonicity. The experiment uncovers a behavioural nuance where contest incentives crowd out an intrinsic inclination to gamble.

This paper experimentally investigates excessive risk taking in contest schemes by implementing a novel stopping task based on Seel and Strack (2013). In this stylized setting, managers with contest payoffs have an incentive to delay halting projects with a negative expectation, with the induced inefficiency being highest for a moderately negative drift. The experiment systematically varies the negative drift (between-subjects) and the payoff incentives (within-subject). We find evidence for excessive risk taking in all our treatment conditions, with the non-monotonicity at least as problematic as predicted. Contrary to the theoretical predictions, this aggregate pattern of behaviour is seen even without contest incentives. Further analysis suggests that many subjects display behaviour consistent with some intrinsic motivation for taking risk. This intrinsic motive and the strategic motive for excessive risk taking reinforce the non-monotonicity. The experiment uncovers a behavioural nuance where contest incentives crowd out an intrinsic inclination to gamble.

We present a general model for the operation of a cloud computing server comprised of one or more speed-scalable processors. Typically, tasks are submitted to such a cloud computing server in an online fashion, and the server operator has to schedule the tasks and decides on payments without knowledge about the tasks arriving in the future. Although very natural, this cloud computing problem on speed-scalable processors has not been studied from a mechanism design perspective in the online setting. We provide a mechanism for this setting, both for a single and multiprocessor environment, that has several desirable properties: (1) the induced game admits a subgame perfect equilibrium in pure strategies and therefore a pure Nash equilibrium, (2) the Price of Anarchy is constant, (3) the mechanism is budget balanced, i.e., the sum of the payments of the agents is equal to the total energy costs, (4) the communication complexity is low, (5) the mechanism is computationally tractable for both the service operator and the agents, and (6) the agents’ payment is also intuitive and easy to communicate to them. We also provide a second mechanism with a better Price of Anarchy, which in turn is more involved to implement. We are able to extend our mechanisms and results to the Bayesian setting, where the type of each agent is drawn independently from some underlying distribution and agents are minimizing their expected costs. In this setting we also show the same approximation factor of our mechanism as in the basic online setting in both the single and the multiprocessor environment.

We present a general model for the operation of a cloud computing server comprised of one or more speed-scalable processors. Typically, tasks are submitted to such a cloud computing server in an online fashion, and the server operator has to schedule the tasks and decides on payments without knowledge about the tasks arriving in the future. Although very natural, this cloud computing problem on speed-scalable processors has not been studied from a mechanism design perspective in the online setting.We provide a mechanism for this setting, both for a single and multiprocessor environment, that has several desirable properties: (1) the induced game admits a subgame perfect equilibrium in pure strategies and therefore a pure Nash equilibrium, (2) the Price of Anarchy is constant, (3) the mechanism is budget balanced, i.e., the sum of the payments of the agents is equal to the total energy costs, (4) the communication complexity is low, (5) the mechanism is computationally tractable for both the service operator and the agents,and (6) the agents’ payment is also intuitive and easy to communicate to them. We also provide a second mechanism with a better Price of Anarchy, which in turn is more involved to implement.We are able to extend our mechanisms and results to the Bayesian setting, where the type of each agent is drawn independently from some underlying distribution and agents are minimizing their expected costs. In this setting we also show the same approximation factor of our mechanism as in the basic online setting in both the single and the multiprocessor environment.

We present a general model for the operation of a cloud computing server comprised of one or more speed-scalable processors. Typically, tasks are submitted to such a cloud computing server in an online fashion, and the server operator has to schedule the tasks and decides on payments without knowledge about the tasks arriving in the future. Although very natural, this cloud computing problem on speed-scalable processors has not been studied from a mechanism design perspective in the online setting. We provide a mechanism for this setting, both for a single and multiprocessor environment, that has several desirable properties: (1) the induced game admits a subgame perfect equilibrium in pure strategies and therefore a pure Nash equilibrium, (2) the Price of Anarchy is constant, (3) the mechanism is budget balanced, i.e., the sum of the payments of the agents is equal to the total energy costs, (4) the communication complexity is low, (5) the mechanism is computationally tractable for both the service operator and the agents, and (6) the agents' payment is also intuitive and easy to communicate to them. We also provide a second mechanism with a better Price of Anarchy, which in turn is more involved to implement. We are able to extend our mechanisms and results to the Bayesian setting, where the type of each agent is drawn independently from some underlying distribution and agents are minimizing their expected costs. In this setting we also show the same approximation factor of our mechanism as in the basic online setting in both the single and the multiprocessor environment.

A Sender wants to persuade multiple Receivers with homogeneous preferences and a common belief about the state of the world to vote in favor of a proposal. Prior to the vote Sender commits to a communication strategy which sends private, potentially correlated, signals to Receivers that are contingent on the true state of the world. While Sender benefits from using private messages rather than public communication if Receivers vote sincerely, under the optimal communication strategy, sincere voting is not in any Receiver’s best interest. If the proposal does not require unanimous agreement, Sender’s optimal communication strategy after which sincere voting indeed constitutes a Bayes-Nash equilibrium is such that no voter is ever pivotal.

A Sender wants to persuade multiple Receivers with homogeneous preferences and a common belief about the state of the world to vote in favor of a proposal. Prior to the vote Sender commits to a communication strategy which sends private, potentially correlated, signals to Receivers that are contingent on the true state of the world. While Sender benefits from using private messages rather than public communication if Receivers vote sincerely, under the optimal communication strategy, sincere voting is not in any Receiver’s best interest. If the proposal does not require unanimous agreement, Sender’s optimal communication strategy after which sincere voting indeed constitutes a Bayes-Nash equilibrium is such that no voter is ever pivotal.

A Sender wants to persuade multiple Receivers with homogeneous preferences and a common belief about the state of the world to vote in favor of a proposal. Prior to the vote Sender commits to a communication strategy which sends private, potentially correlated, signals to Receivers that are contingent on the true state of the world. While Sender benefits from using private messages rather than public communication if Receivers vote sincerely, under the optimal communication strategy, sincere voting is not in any Receiver’s best interest. If the proposal does not require unanimous agreement, Sender’s optimal communication strategy after which sincere voting indeed constitutes a Bayes-Nash equilibrium is such that no voter is ever pivotal.

Subgame perfect equilibrium in stationary strategies (SSPE) is the most important solution concept used in applications of stochastic games, which makes it imperative to develop efficient numerical methods to compute an SSPE. For this purpose, this paper develops an interior-point path-following method (IPM), which remedies a number of issues with the existing method called stochastic linear tracing procedure (SLTP). The homotopy system of IPM is derived from the optimality conditions of an artificial barrier game, whose objective function is a combination of the original payoff function and a logarithmic term. Unlike SLTP, the starting stationary strategy profile can be arbitrarily chosen and IPM does not need switching between different systems of equations. The use of a perturbation term makes IPM applicable to all stochastic games, whereas SLTP only works for a generic stochastic game. A transformation of variables reduces the number of equations and variables of by roughly one half. Numerical results show that our method is more than three times as efficient as SLTP.

Subgame perfect equilibrium in stationary strategies (SSPE) is the most important solution concept used in applications of stochastic games, which makes it imperative to develop efficient numerical methods to compute an SSPE. For this purpose, this paper develops an interior-point path-following method (IPM), which remedies a number of issues with the existing method called stochastic linear tracing procedure (SLTP). The homotopy system of IPM is derived from the optimality conditions of an artificial barrier game, whose objective function is a combination of the original payoff function and a logarithmic term. Unlike SLTP, the starting stationary strategy profile can be arbitrarily chosen and IPM does not need switching between different systems of equations. The use of a perturbation term makes IPM applicable to all stochastic games, whereas SLTP only works for a generic stochastic game. A transformation of variables reduces the number of equations and variables of by roughly one half. Numerical results show that our method is more than three times as efficient as SLTP.

Subgame perfect equilibrium in stationary strategies (SSPE) is the most important solution concept used in applications of stochastic games, which makes it imperative to develop efficient numerical methods to compute an SSPE. For this purpose, this paper develops an interior-point path-following method (IPM), which remedies a number of issues with the existing method called stochastic linear tracing procedure (SLTP). The homotopy system of IPM is derived from the optimality conditions of an artificial barrier game, whose objective function is a combination of the original payoff function and a logarithmic term. Unlike SLTP, the starting stationary strategy profile can be arbitrarily chosen and IPM does not need switching between different systems of equations. The use of a perturbation term makes IPM applicable to all stochastic games, whereas SLTP only works for a generic stochastic game. A transformation of variables reduces the number of equations and variables of by roughly one half. Numerical results show that our method is more than three times as efficient as SLTP.