The order of stages in a multistage game is often interpreted by looking at earlier stages as involving more long term decisions. For the purpose of making this interpretation precise, the notion of a delay supergame of a bounded multistage game is introduced. A multistage game is bounded if the length of play has an upper bound. A delay supergame is played over many periods. Decisions on all stages are made simultaneously, but with different delays until they become effective. The (...) earlier the stage the longer the delay. A subgame perfect equilibrium of a bounded multistage game generates a subgame perfect equilibrium in every one of its delay supergames. This is the first main conclusion of the paper. A subgame perfect equilibrium set is a set of subgame perfect equilibria all of which yield the same payoffs, not only in the game as a whole, but also in each of its subgames. The second xmain conclusion concerns multistage games with a unique subgame perfect equilibrium set and their delay supergames which are bounded in the sense that the number of periods is finite. If a bounded multistage game has a unique subgame perfect equilibrium set, then the same is true for every one of its bounded delay supergames. Finally the descriptive relevance of multistage game models and their subgame perfect equilibria is discussed in the light of the results obtained. (shrink)

Unlike the supergame model assumes agents in exchange situations will normally not be perfectly informed on past behaviour of their partners. Also, they will be able to choose their partners to a certain extend. A formal model is presented that attempts to take account of these facts. It is supposed that for any actor the probability of finding a partner for a lucrative exchange depends on his past behaviour. A model of reputation formation is presented as a formal description of (...) this interdependency. Based on this model it is shown that under certain conditions only co-operative conduct will pay in the long run. Thus it is confirmed that - given the mechanism of trust - rational agents may act trustworthy. (shrink)

The extent to which trust prevails can be measured by the subjective probability with which an agent expects another one to act in desired ways. An agent´s trust in other agents forms in repeated social interactions which typically have the structure of an elementary game of trust. The process of trust formation in such interactions may be described by a reputation function. It is argued that in view of real world processes of trust formation any adequate reputation function must satisfy (...) certain conditions. A simple model conforming to these conditions is presented. Analysing this example it is shown that there is a co-operative Nash equilibrium in a trust supergame which is in line with the basic conditions of trust formation. However, it is also proved that no process of trust formation can be reasonably similar to real world mechanisms and at the same time lead to subgame perfect equilibria in a trust supergame. (shrink)

This 1987 book offers a critique of the liberal theory of the state, focusing on a detailed study of cooperation in the absence of the state and of other kinds of coercion. The discussion includes an analysis of collective action and of the Prisoners' Dilemma supergame. It is a revised and expanded edition of the author's classic work of rational choice theory Anarchy and Cooperation, originally published with John Wiley in 1976. The analysis has been recast and developed here to (...) make it more accessible to non-mathematical readers and to provide a more comprehensive and self-contained treatment of the theory of collective action. The book will be of interest to a range of readers in political and social philosophy and in economics. (shrink)

This book uses game theory to analyse the creation, evolution and function of economic and social institutions. The author illustrates his analysis by describing the organic or unplanned evolution of institutions such as the conventions of war, the use of money, property rights and oligopolistic pricing conventions. Professor Schotter begins by linking his work with the ideas of the philosophers Rawls, Nozick and Lewis. Institutions are regarded as regularities in the behaviour of social agents, which the agents themselves tacitly create (...) to solve a wide variety of recurrent problems. The repetitive nature of the problems permits them to be described as a recurrent game or 'supergame.' The agents use these regularities as informational devices to supplement the information contained in competitive prices. The final chapter explores the applicability of this theory, first by relating it to previous work on the theory of teams, hierarchies, and non-maximizing decision theory, and then by using it to provide a new approach to a variety of questions both within and outside economics. (shrink)

We introduce a novel mechanism to eliminate endgame effects in repeated prisoner’s dilemma experiments. In the main phase of a supergame our mechanism generates more persistent cooperation than finite horizon or random continuation rules. Moreover, we find evidence for cooperation-enhancing “active/reactive” strategies which concentrate in the initial phase of a supergame as subjects gain experience.

Experiments in which subjects play simultaneously several finite two-person prisoner's dilemma supergames with and without an outside option reveal that: an attractive outside option enhances cooperation in the prisoner's dilemma game, if the payoff for mutual defection is negative, subjects' tendency to avoid losses leads them to cooperate; while this tendency makes them stick to mutual defection if its payoff is positive, subjects use probabilistic start and endeffect behavior.

The theory of games, though at first greeted with great expectations by some social scientists, soon became a source of frustrated hopes to many of them. Too much of the theory seemed to be devoted to “zero-sum” and “one-shot” games. But most social contexts are not zero-sum and involve repeated interaction too. There was a certain lack of such game theoretic models which could be successfully adapted to social phenomena as were apt to appear in reality. Recently the theory of (...) games seems to be on its way to closing this gap within a special branch devoted to “repeated games” or “supergames”. Very promising is the approach of Michael Taylor which is surveyed and discussed in the subsequent paper. This approach has two main merits: First it can be understood with a modest mathematical background, secondly it can be adapted easily to a more precise reconstruction of classical topics in political theory. Though one might not agree with some of Taylor’s conclusions it seems to be worthwhile to get acquainted at least with the basics of his analysis and to take it as a first step to opening avenues for future social research. (shrink)

In contrast to Axelrod’s advice “don’t be envious” it is argued that the emotion of envy may enhance cooperation. TIT FOR TAT does exhibit a certain degree of envy. But, it does so in inconsistent ways. Two variants of TIT FOR TAT are introduced and their strategic properties are analyzed. Both generate the very same actual play as TIT FOR TAT in a computer tournament without noise. However, if noise is introduced they display some greater degree of stability. This is (...) due to the fact that they form, in a prisoner’s dilemma supergame with suitable parameters, an equilibrium with themselves that is subgame perfect or (in case of the first strategy) close to subgame perfect. It is additionally argued that these strategies are exceptionally clear and comprehensible to others in that they conform to well known real live behavior patterns. (shrink)

Two institutions that are often implicit or overlooked in noncooperative games are the assumption of Nash behavior to solve a game, and the ability to correlate strategies. We consider two behavioral paradoxes; one in which maximin behavior rules out all Nash equilibria (‘Chicken’), and another in which minimax supergame behavior leads to an ‘inefficient’ outcome in comparison to the unique stage game equilibrium (asymmetric ‘Deadlock’). Nash outcomes are achieved in both paradoxes by allowing for correlated strategies, even when individual behavior (...) remains minimax or maximin. However, the interpretation of correlation as a public institution differs for each case. (shrink)

Two institutions that are often implicit or overlooked in noncooperative games are the assumption of Nash behavior to solve a game, and the ability to correlate strategies. We consider two behavioral paradoxes; one in which maximin behavior rules out all Nash equilibria (‘Chicken’), and another in which minimax supergame behavior leads to an ‘inefficient’ outcome in comparison to the unique stage game equilibrium (asymmetric ‘Deadlock’). Nash outcomes are achieved in both paradoxes by allowing for correlated strategies, even when individual behavior (...) remains minimax or maximin. However, the interpretation of correlation as a public institution differs for each case. (shrink)