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We analyze reputation effects in two-player repeated games of strictly conflicting interests. In such games player 1 has a commitment action such that a best reply to it gives player 1 the highest individually rational payoff and player 2 the minmax payoff. Players have equal discount factors. With positive probability player 1 is a type who chooses the commitment action after every history. We show that player 1’s payoff converges to the maximally feasible payoff when the discount factor converges to one. This contrasts with failures of reputation effects for equal discount factors that have been demonstrated in the literature. Journal of Economic Literature Classification Number: C71.

I consider an alternating offer bargaining game which is played by a risk neutral buyer and seller, where the value of the good to be traded follows a Markov process. For these games the existence of a perfect equilibrium is proved and the set of equilibrium payoffs and strategies are characterised. The main results are (a) if the buyer is less patient than the seller, then there will be delays in the players reaching an agreement, the buyer is forced into a suboptimal consumption policy and the equilibrium is ex-ante inefficient, and (b) if the buyer is more patient than the seller, then there is a unique and efficient equilibrium where agreement is immediate.

The paper analyzes reputation effects in general perturbed repeated games with discounting. If there is some positive prior probability that one of the players is committed to play the same (pure or mixed) action in every period, then this provides a lower bound for her equilibrium payoff in all Nash equilibria. This bound is tight and independent of what other types have positive probability. It is generally lower than Fudenberg and Levine's (1989, 1992) bound for games with a long-run player facing a sequence of short-run opponents. The bound cannot be improved by considering types playing history dependent commitment strategies.

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. Will the agents commonly learn the value of the parameter, i.e., will the true value of the parameter become approximate common-knowledge? If the signals are independent and identically distributed across time (but not necessarily across agents), the answer is yes (Cripps, Ely, Mailath, and Samuelson, 2008). This paper explores the implications of allowing the signals to be dependent over time. We present a counterexample showing that even extremely simple time dependence can preclude common learning, and present sufficient conditions for common learning.

There has been significant interest recently both in the empirical investigation of the determinants of trade union membership, in the U.K. and elsewhere, and in the theoretical analysis of the economic effects of the closed shop trade union. However, there is little rigorous microeconomic explanation of union membership which is relevant for much of the U.K. and similar labour markets where the ‘open shop’ union is prevalent. This paper attempts to overcome the free-rider problem of explaining union membership in the open shop. We argue that both private pecuniary gains and social influences affect the individuals' union membership decisions, citing evidence in support of these basic assumptions. We show that stable intermediate union density is a possible equilibrium outcome in a generalised social custom model. We also analyse the simultaneous determination of wages and union membership, deriving a number of comparative static results. In particular, we find that both wages and union density depend upon, inter alia, the level of strike pay, the net cost of union membership and the individual's sensitivity to social custom and associated solidarity effects. We argue that the approach is consistent with various stylised facts concerning both wage bargaining and union membership and is able to explain a number of otherwise puzzling features of union membership.

The widespread use of parallel machines has been hampered by the difficulty of mapping applications onto them effectively. The difficulty arises because current programming languages require the programmer to specify a problem to be solved at a low level of abstraction in an imperative form. Thus the programmer must immediately encode an architecture-specific algorithm detailing every communication and calculation. This process is prone to error and complicates the reuse of software. An alternative approach is to specify the problem to be solved at a high-level in a functional language. Meaning-preserving program transformations can then be used to derive a parallel algorithm. Such algorithms can be run on parallel graph-reduction or dataflow machines which automatically exploit the implicit parallelism in a functional language program. Such automatic decomposition techniques, however, are not yet capable of fully yielding the extra performance offered by the parallel hardware. We show how, by including an architecture specification with the problem specification, and extending the amount of transformation performed, it is possible to produce functional language code that explicity expresses the calculations and communications to be performed by the processors. This simplifies compilation, yields faster programs and enables parallel software to be developed for a wide variety of parallel computer architectures. A goal-seeking transformation methodology has been developed which enables a high-level functional specification of the problem and a high-level functional abstraction of the target computer architecture to be systematically manipulated to produce an efficient parallel algorithm tailored to the target architecture. As the transformations start from very high-level specifications, the discovery of new algorithms is facilitated. A case study is used to demonstrate the effectiveness of the technique. We show how a high level specification for sort can be transformed with a pipeline architecture specification to give a mergesort and how the same specification with a dynamic-message-passing architecture specification can be transformed to a novel parallel quicksort.

There is a considerable body of work which shows that the set of outcomes from rational play in a game is identical to a set of correlated equilibria. We show that the set of outcomes from evolutionary stable behavior, where nature serves as a correlating device, is identical to the set of strict correlated equilibria. This extends the result that ESS corresponds to strict Nash equilibrium, provided by R. Selten (Math. Social Sci. 5, 1983, 269–363), by allowing for correlation.

For games of public reputation with uncertainty over types and imperfect public monitoring, Cripps, Mailath, and Samuelson (2004) showed that an informed player facing short-lived uninformed opponents cannot maintain a permanent reputation for playing a strategy that is not part of an equilibrium of the game without uncertainty over types. This paper extends that result to games in which the uninformed player is long-lived and has private beliefs, so that the informed player's reputation is private.

For games of public reputation with uncertainty over types and imperfect public monitoring, Cripps, Mailath, and Samuelson (2004) showed that an informed player facing short-lived uninformed opponents cannot maintain a permanent reputation for playing a strategy that is not part of an equilibrium of the game without uncertainty over types. This paper extends that result to games in which the uninformed player is long-lived and has private beliefs, so that the informed player's reputation is private. We also show that the rate at which reputations disappear is uniform across equilibria and that reputations disappear in sufficiently long discounted finitely-repeated games.

We study the long-run sustainability of reputations in games with imperfect public monitoring. It is impossible to maintain a permanent reputation for playing a strategy that does not play an equilibrium of the game without uncertainty about types. Thus, a player cannot indefinitely sustain a reputation for non-credible behavior in the presence of imperfect monitoring.

This paper studies a game of strategic experimentation with two-armed bandits whose risky arm might yield a payoff only after some exponentially distributed random time. Because of free-riding, there is an inefficiently low level of experimentation in any equilibrium where the players use stationary Markovian strategies with posterior beliefs as the state variable. After characterizing the unique symmetric Markovian equilibrium of the game, which is in mixed strategies, we construct a variety of pure-strategy equilibria. There is no equilibrium where all players use simple cut-off strategies. Equilibria where players switch finitely often between the roles of experimenter and free-rider all lead to the same pattern of information acquisition; the efficiency of these equilibria depends on the way players share the burden of experimentation among them. In equilibria where players switch roles infinitely often, they can acquire an approximately efficient amount of information, but the rate at which it is acquired still remains inefficient; moreover, the expected payoff of an experimenter exhibits the novel feature that it rises as players become more pessimistic. Finally, over the range of beliefs where players use both arms a positive fraction of the time, the symmetric equilibrium is dominated by any asymmetric one in terms of aggregate payoffs.

We study the long-run sustainability of reputations in games with imperfect public monitoring. It is impossible to maintain a permanent reputation for playing a strategy that does not eventually play an equilibrium of the game without uncertainty about types. Thus, a player cannot indefinitely sustain a reputation for non-credible behavior in the presence of imperfect monitoring.

This paper introduces a dynamic model of the wealth distribution with aggregate risk in the capital market; the model combines credit rationing and portfolio selection decisions. In a closed economy the long-run behaviour of wealth is independent of the initial income distribution when there is aggregate uncertainty, although further restrictions are necessary when there is no aggregate uncertainty. There can be credit rationing at the long-run equilibrium. In poor economies aggregate risk in the capital market slows growth, whereas in richer economies a risky capital market is good for income growth.

Much work has been carried out within the last few years to link together "islands of automation" on a factory floor using local area networks. This has led to the development of standards in communication systems, such as the Manufacturing Automation Protocol sponsored by the General Motors Corporation. At present a standard, low-cost approach to implementing manufacturing systems, ensuring compatability with the higher-cost MAP-based systems, is not available. If such a standard were available then small firms could install distributed automation control systems incrementally. This paper describes the application of multi-level, hierarchical control to a simple assembly flow line for the consumer electronics industry. There are four basic levels in the system, the lowest being an assembly operation carried out by human or robotic operators. A number of separate assembly operations, each controlled by work station controllers, are formed into a flow line with a number of flow lines forming the complete manufacturing facility controlled by a Computer Aided Manufacture (CAM) host. It is only at the level of the flow line controller and above that the MAP protocols can be applied cost-effectively in a small manufacturing environment. Adoption of the hierarchical approach throughout the system ensures that it is flexible, reliable, easily maintained and can be installed incrementally. The standardisation of low-cost local area networks (LANs) to interconnect the programmable logic controllers (PLCs) is crucial to this task because the lower level communication can then be implemented at much reduced cost as the performance required is minimised. An analysis of the requirements and implementations of LANs for this purpose is provided. To ensure correct operation of the workstation controllers and the associated communication to their flow line controller, a complete and novel Petri-net based logic controller design (PNLC) has been tested. This allows emulation and simulation of algorithms in the stations, to prove both the algorithms and their intercommunication are correct, prior to direct transfer to running on the factory floor.