We examine learning in all experiments we could locate involving 100 periods or more of games with a unique equilibrium in mixed strategies, and in a new experiment. We study both the ex post ( "best fit") descriptive power of learning models, and their ex ante predictive power, by simulating each experiment using parameters estimated from the other experiments. Even a one-parameter reinforcement learning model robustly outperforms the equilibrium predictions. Predictive power is improved by adding "forgetting" and "experimentation, " or by allowing greater rationality as in probabilistic fictitious play. Implications for developing a low-rationality, cognitive game theory are discussed. (JEL C72, C92)

Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria

New Patterns of Management.

Players in a game are “in equilibrium” if they are rational, and accurately predict other players' strategies. In many experiments, however, players are not in equilibrium. An alternative is “cognitive hierarchy” (CH) theory, where each player assumes that his strategy is the most sophisticated. The CH model has inductively defined strategic categories: step 0 players randomize; and step k thinkers best-respond, assuming that other players are distributed over step 0 through step k − 1. This model fits empirical data, and explains why equilibrium theory predicts behavior well in some games and poorly in others. An average of 1.5 steps fits data from many games.

/pdf/a-cognitive-hierarchy-model-of-games-59s1sbbd6p.pdf

A Cognitive Hierarchy Model of Games

Society for Industrial and Applied Mathematics(SIAM)

Game theoretic analysis of a bankruptcy problem from the Talmud

http://darp.lse.ac.uk/papersDB/O'Neill_(MASS82).pdf

A problem of rights arbitration from the Talmud

As an experimental test of the minimax theory for two-person zerosum games, subjects played a game that was especially easy for them to understand and whose minimax-prescribed solution did not depend on quantitative assumptions about their utilities for money. Players' average relative frequencies for the moves and their proportions of wins were almost exactly as predicted by minimax, but subject-to-subject variability was too high. These results suggest that people can deviate somewhat from minimax play since their opponents have limited information-processing ability and are imperfect record keepers, but they do not stray so far that the difference will be noticed and their own payoffs will be diminished.

https://www.pnas.org/content/pnas/84/7/2106.full.pdf

Nonmetric test of the minimax theory of two-person zerosum games.

/Vfter atrocities, disappearances, and other human rights violations, the dictatorship in Authoritania falls, and a new democratic regime takes power, changing the coun try's name to Freedonia. How should Freedonia deal with Authoritania's rulers and their agents? Do they have options between forgiveness and full-scale retribution? Should agents of the past regime be allowed political rights? Should victims be com pensated, and should confiscated property be restored? What role does the interna tional community have? These kinds of dilemmas constitute the field of transitional justice. Transitional jus tice refers to formal and informal procedures implemented by a group or institution of accepted legitimacy around the time of a transition out of an oppressive or violent social order, for rendering justice to perpetrators and their collaborators, as well as to their victims. Following Elster (2004), we divide transitional justice into endogenous and exogenous. In the endogenous case, the procedures are administered by the society itself, without external intervention. Exogenous transitional justice is administered from the outside, typically by agents who were not engaged in the conflict, and often

https://www.jstor.org/stable/info/27638491

Normative and Strategic Aspects of Transitional Justice

http://pluto.mscc.huji.ac.il/~mswiener/research/GradualBargaining.pdf

Bargaining with an agenda

Leaders and historians see prestige as important, but international relations theorists have neglected the concept, in part for lack of a clear definition. It is proposed that a party holds prestige when group members generally believe that the party has a certain desirable quality, and this situation gives the party perceived power in the group. The definition gains support from a survey of international affairs writings on the sources of prestige. Prestige is strategically important when a party wants support from others who would rather join the side that more of the others are joining. Some general ways of acquiring prestige are discussed. Compared to achieving social progress, building and testing nuclear weapons is better at bearing prestige because it has distinct borders separating success and failure, because it is salient and because it involves the symbolism of power. In some cases when prestige is a factor, one can better demonstrate one's ability to perform an accomplishment by refraining from doing it. The analysis yields suggestions for reducing nuclear proliferation.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID887333_code331494.pdf?abstractid=887333&mirid=1&type=2

Barry O'Neill

Papers

A problem of rights arbitration from the Talmud

Nonmetric test of the minimax theory of two-person zerosum games.

Normative and Strategic Aspects of Transitional Justice

Bargaining with an agenda

Nuclear Weapons and National Prestige