Payoff dominance and the Stackelberg heuristic

2002

Satisficing, or being "good enough," is the fundamental obligation of rational decision makers. We cannot rationally choose an option, even when we do not know of anything better, unless we know it is good enough. Unfortunately, we are not often in the position of knowing that there could be no better option, and hence that the option must be good enough. A complete search through all logical possibilities is often impractical, particularly in multi-agent contexts, due to excessive computational difficulty, modeling complexity, and uncertainty. It can be equally impractical, if it is even possible, to determine the cost of the additional required search to find an option that is good enough. In a departure from the traditional notion of satisficing as a species of bounded rationality, satisficing is here redefined in terms of a notion of intrinsic rationality. Epistemic utility theory serves as the philosophical foundation of a new praxeological decision-making paradigm of satisficing equilibria that is applicable to both single-and multiple-agent scenarios. All interagent relationships are modeled by an interdependence function that explicitly accommodates both self and group interest, from which multilateral and unilateral selectability and rejectability mass functions can be derived and compared via the praxeic likelihood ratio test.

Decision, 2014

Social projection cannot adequately explain coordination in common interest games, and nothing resembling social projection underlies team reasoning or strong Stackelberg reasoning. Although our experiments suggest that cognitive hierarchy Level-1 reasoning was most influential in the games that we investigated, strong Stackelberg reasoning and team reasoning were also used quite frequently by the players.

Decision, 2014

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In common interest games, players generally manage to coordinate their actions on mutually optimal outcomes, but orthodox game theory provides no reason for them to play their individual parts in these seemingly obvious solutions and no justification for choosing the corresponding strategies. A number of theories have been suggested to explain coordination, among the most prominent being versions of cognitive hierarchy theory, theories of team reasoning, and social projection theory (in symmetric games). Each of these theories provides a plausible explanation but is theoretically problematic. An improved theory of strong Stackelberg reasoning avoids these problems and explains coordination among players who care about their co-players' payoffs and who act as though their co-players can anticipate their choices. Two experiments designed to test cognitive hierarchy, team reasoning, and strong Stackelberg theories against one another in games without obvious, payoff-dominant solutions suggest that each of the theories provides part of the explanation. Cognitive hierarchy Level-1 reasoning, facilitated by a heuristic of avoiding the worst payoff, tended to predominate, especially in more complicated games, but strong Stackelberg reasoning occurred quite frequently in the simpler games and team reasoning in both the simpler and the more complicated games. Most players considered two or more of these reasoning processes before choosing their strategies.

Behavioral and Brain Sciences, 2003

Psychological game theory encompasses formal theories designed to remedy game-theoretic indeterminacy and to predict strategic interaction more accurately. Its theoretical plurality entails second-order indeterminacy, but this seems unavoidable. Orthodox game theory cannot solve payoff-dominance problems, and remedies based on interval-valued beliefs or payoff transformations are inadequate. Evolutionary game theory applies only to repeated interactions, and behavioral ecology is powerless to explain cooperation between genetically unrelated strangers in isolated interactions. Punishment of defectors elucidates cooperation in social dilemmas but leaves punishing behavior unexplained. Team reasoning solves problems of coordination and cooperation, but aggregation of individual preferences is problematic. I am grateful to commentators for their thoughtful and often challenging contributions to this debate. The commentaries come from eight different countries and an unusually wide range of disciplines, including psychology, economics, philosophy, biology, psychiatry, anthropology, and mathematics. The interdisciplinary character of game theory and experimental games is illustrated in Lazarus's tabulation of more than a dozen disciplines studying cooperation. The richness and fertility of game theory and experimental games owe much to the diversity of disciplines that have contributed to their development from their earliest days. The primary goal of the target article is to argue that the standard interpretation of instrumental rationality as expected utility maximization generates problems and anomalies when applied to interactive decisions and fails to explain certain empirical evidence. A secondary goal is to outline some examples of psychological game theory, designed to solve these problems. Camerer suggests that psychological and behavioral game theory are virtually synonymous, and I agree that there is no pressing need to distinguish them. The examples of psychological game theory discussed in the target article use formal methods to model reasoning processes in order to explain powerful intuitions and empirical observations that orthodox theory fails to explain. The general aim is to broaden the scope and increase the explanatory power of game theory, retaining its rigor without being bound by its specific assumptions and constraints. Rationality demands different standards in different domains. For example, criteria for evaluating formal arguments and empirical evidence are different from standards of rational decision making (Manktelow & Over 1993; Nozick 1993). For rational decision making, expected utility maximization is an appealing principle but, even when it is combined with consistency requirements, it does not appear to provide complete and intuitively convincing prescriptions for rational conduct in all situations of strategic interdependence. This means that we must either accept that rationality is radically and permanently limited and riddled with holes, or try to plug the holes by discovering and testing novel principles. In everyday life, and in experimental laboratories, when orthodox game theory offers no prescriptions for choice, people do not become transfixed like Buridan's ass. There are even circumstances in which people reliably solve problems of coordination and cooperation that are insoluble with the tools of orthodox game theory. From this we may infer that strategic interaction is governed by psychological game-theoretic principles that we can, in principle, discover and understand. These principles need to be made explicit and shown to meet minimal standards of coherence, both internally and in relation to other plausible standards of rational behavior. Wherever possible, we should test them experimentally. In the paragraphs that follow, I focus chiefly on the most challenging and critical issues raised by commentators. I scrutinize the logic behind several attempts to show that the problems discussed in the target article are spurious or that they can be solved within the orthodox theoretical framework, and I accept criticisms that appear to be valid. The commentaries also contain many supportive and elaborative observations that speak for themselves and indicate broad agreement with many of the ideas expressed in the target article. I am grateful to Hausman for introducing the important issue of rational beliefs into the debate. He argues that games can be satisfactorily understood without any new interpretation of rationality, and that the anomalies and problems that arise in interactive decisions can be eliminated by requiring players not only to choose rational strategies but also to hold rational beliefs. The only requirement is that subjective probabilities "must conform to the calculus of probabilities." Rational beliefs play an important role in Bayesian decision theory. Kreps and Wilson (1982b) incorporated them into a refinement of Nash equilibrium that they called perfect Bayesian equilibrium, defining game-theoretic equilibrium for the first time in terms of strategies and beliefs. In perfect Bayesian equilibrium, strategies are best replies to one another, as in standard Nash equilibrium, and beliefs are sequentially rational in the sense of specifying actions that are optimal for the players, given those beliefs. Kreps and Wilson defined these notions precisely using the conceptual apparatus of Bayesian decision theory, including belief updating according to Bayes' rule. These ideas prepared the ground for theories of rationalizability (Bernheim 1984; Pearce 1984), discussed briefly in section 6.5 of the target article, and the psychological games of Geanakoplos et al. (1989), to which I shall return in section R7 below. Hausman invokes rational beliefs in a plausible -though I believe ultimately unsuccessful -attempt to solve the payoff-dominance problem illustrated in the Hi-Lo Matching game (Fig. in the target article). He acknowledges that a player cannot justify choosing H by assigning particular probabilities to the co-player's actions, because this leads to a contradiction (as explained in section 5.6 of the target article). 1 He therefore offers the following suggestion: "If one does not require that the players have point priors, then Player I can believe that the probability that Player II will play H is not less than one-half, and also believe that Player II believes the same of Player I. Player I can then reason that Player II will definitely play H, update his or her subjective probability accordingly, and play H." This involves the use of interval-valued (or set-valued) probabilities, tending to undermine Hausman's claim that it "does not need a new theory of rationality." Intervalvalued probabilities have been axiomatized and studied ), but they are problematic, partly because stochastic independence, on which the whole edifice of probability theory is built, cannot be satisfactorily defined for them, and partly because technical problems arise when Bayesian updating is applied to interval-valued priors. Leaving these problems aside, the proposed solution cleverly eliminates the contradiction that arises when a player starts by specifying a point probability,

Keio economic studies, 1980

We regard a leader in the Stackelberg disequilibrium as a duopolist who decides his output level before-his rival's decision and then informs him of it, and regard a follower as one who waits to be informed of it and then decides his output level under the information. We formulate this situation as a game in extensive form and provide the subgame perfect equilibrium of the game to give an interpretation to the Stackelberg disequilibrium. Further we discuss a variation of the game. Notes Genre Journal Article URL .

Standard game theory cannot explain the selection of payoff-dominant outcomes that are best for all players in common-interest games. Theories of team reasoning can explain why such mutualistic cooperation is rational. They propose that teams can be agents and that individuals in teams can adopt a distinctive mode of reasoning that enables them to do their part in achieving Pareto-dominant outcomes. We show that it can be rational to play payoff-dominant outcomes, given that an agent group identifies. We compare team reasoning to other theories that have been proposed to explain how people can achieve payoff-dominant outcomes, especially with respect to rationality. Some authors have hoped that it would be possible to develop an argument that it is rational to group identify. We identify some large-probably insuperable-problems with this project and sketch some more promising approaches, whereby the normativity of group identification rests on morality.

Handbook of Game Theory with Economic Applications, 2015

2007

Noncooperative games are examined from the point of view of an outside observer who believes that the players are rational and that they know at least as much as the observer. The observer is assumed to be able to observe many instances of the play of the game; these instances are identical in the sense that the observer cannot distinguish between the settings in which different plays occur. If the observer does not believe that he will be able to offer beneficial advice then he must believe that the players are playing a correlated equilibrium, though he may not initially know which correlated equilibrium. If the observer also believes that, in a certain sense, there is nothing connecting the players in a particular instance of the game then he must believe that the correlated equilibrium they are playing is, in fact, a Nash equilibrium.

Games and Economic Behavior, 2009

We report experimental results on one-shot two person 3x3 constant sum games played by non-economists without previous experience in the laboratory. Although strategically our games are very similar to previous experiments in which game theory predictions fail dramatically, 80% of actions taken in our experiment coincided with the prediction of the unique Nash equilibrium in pure strategies and 73% of actions were best responses to elicited beliefs. We argue how social preferences, presentation e¤ects and belief elicitation procedures may in ‡uence how subjects play in simple but non trivial games and explain the di¤erences we observe with respect to previous work.