Unit IV: Thinking about Thinking Behavioral Game Theory Learning to Cooperate Summary and Conclusions 8/4

Summary and Conclusions The Logic of Collective Action The Problem of Trust The Limits of Strategic Rationality The Evolution of Game Theory Tournament Update and Demonstration

The Logic of Collective Action “[T]he achievements of a union, even if they were more impressive than the staunchest unionist claims, could offer the rational worker no incentive to join; his individual efforts would have no noticeable effect on the outcome, and whether he supported the union or not he would still get the benefit of its achievement.” - Olson, 1965, p. 76.

“Given a Prisoner’s Dilemma such as trade union formation, it can be argued that prolonged interaction between the workers will make the real payoff structure diverge from the purely monetary one, because the welfare of others will enter into the utility function of the individual. This could change the game into an Assurance Game […] sustained interaction in such communities may do away with the problem itself by transforming the nature of the game.” - Elster 1979, p.146. The Logic of Collective Action

Prisoner’s Dilemma Assurance Game 6, 6 0, 5 5, 0 1, 1 3, 3 0, 5 5, 0 1, 1

The Logic of Collective Action Repeated interaction is a necessary but not a sufficient condition for cooperation. To cooperate, those involved must regard the outcome as fair, and this may be subverted by strategic attempts to manipulate the process. From this point of view, trust can be seen as the problem to be solved.

A thought experiment. Workers in a young industry consider the option of forming a union. A meeting is held and a vote is called. A majority oppose. A worker known to have been an instigator stands and speaks: “Brothers and sisters, do not let your petty differences stand in the way of our purpose. Workers – all of us – are called upon to unite against a common enemy: the bosses who exploit us and grow fat off our divisiveness. Together we possess a might they cannot ignore; alone we fight – one against another – for the scraps that fall from their tables.” The Logic of Collective Action the Common Enemy

The Logic of Collective Action “No union can function for a day in the absence of some rudimentary notions held by the members that being a member is of value in itself, that the individual organization costs … have to be accepted as necessary sacrifices, and that each member is legitimately required to practise solidarity and discipline…. ” (Offe and Wiesenthal, 1980, p. 184). Two s

The Logic of Collective Action “The logic of collective action of the relatively powerless differs from that of the relatively powerful in that the former implies a paradox that is absent from the latter - the paradox that interests can only be met to the extent they are partly redefined.” (Offe and Wiesenthal, 1980, p. 184). Two s

Changing the Rules of the Game On the one hand, a game of strategy is defined by its rules, and the assumption of strategic rationality supposes that each player is following preferences and decision procedures that he has determined for himself -- that is, monologically, regardless of whether or not he agrees therein with the other players. In non-zero sum games there are mutual gains to be had if a bargain is achieved, but the entire process takes place within a set of predetermined and irreducibly opposed interests, or preferences.

On the other hand, changing the rules of the game requires that the players first try to understand each other, and in so doing come to understand their own positions in a new light, reflected in the accounts and descriptions offered by others. Instead of bargaining from the relative strength of their interest positions and achieving a compromise, circumscribed by their given positions, they may even redefine their preferences. Changing the Rules of the Game

From this point of view, trust can be seen as the problem to be solved. It is no simple matter to provide reasons for each other’s trust – why one should be believed to mean what is said and intend what is proposed – but to change the rules of the game, those involved must regard the terms of their agreement as fair, as mutually binding, and this may be subverted by strategic attempts to manipulate the process. Changing the Rules of the Game

The Problem of Trust is a “social lubricant” (Arrow, 1974, p. 23). It’s easier to make efficient exchanges (transactions costs are lower) when trust is higher. is a reciprocal expectation; it’s hard to trust other(s) without thinking yourself trustworthy. So is the absence of trust; I may fear you will betray me not because I believe you are untrustworthy, but because I know I am. may confer an evolutionary advantage on groups. is a state that cannot be willed. Trust

Rational analysis, for all its inadequacies, is indeed the best instrument of cognition we have. But it is often at its best when it reveals to us the nature of the situation we find ourselves in, even though it may have nothing to tell us how we ought to behave in this situation. Too much depends upon our choice of values, criteria, notions of what is “rational,” and, last by but no means least, the sort of relationship and communication we establish with the other parties in the “game.” (Rapoport, 1960, p. 214). The Limits of Strategic Rationality

These choices have nothing to do with the particular game we are playing. They are not strategic choices, i.e., choices rationalized in terms of the benefits they bestow on us in a particular conflict. Rather they are choices which we make because of the way we view ourselves, and the world, including the other players. The great philosophical value of game theory is its ability to reveal its own incompleteness. Game- theoretical analysis, if pursued to its completion, perforce leads us to consider other than strategic modes of thought (Rapoport, 1960, p. 214). The Limits of Strategic Rationality

Game theory was developed to “solve” simple parlor games. In the 1940s and ‘50s, it was applied to international conflict A THEORY OF WAR Schelling “reoriented” game theory to seek ways of resolving conflict as an alternative to war. In the Post-war period, attention turned to expanding trade among Western economies EXCHANGE The Prisoner’s Dilemma exposed a deep problem at the heart of game theory, calling forth a new approach. Finally, analysis of repeated games offered a way to understand today’s global problems COOPERATION The Evolution of Game Theory

ZEROSUM GAMESNONZEROSUM GAMESREPEATED GAMES MINIMAX THEOREMNASH EQUILIBRIUMFOLK THEOREM PRISONER’S DILEMMA WAR EXCHANGECOOPERATION PARLOR GAMESNUCLEAR TRADE SUSTAINABLE ARMS RACE DEVELOPENT Theory of Games Strategy & ConflictThe Evolution & Economic Behavior of Cooperation Soviet A-TestThe End of the Cold War Nobel: Harsanyi, Selten & Nash The Evolution of Game Theory

ZEROSUM GAMESNONZEROSUM GAMESREPEATED GAMES MINIMAX THEOREMNASH EQUILIBRIUMFOLK THEOREM PRISONER’S DILEMMA WAR EXCHANGECOOPERATION PARLOR GAMESNUCLEAR TRADE SUSTAINABLE ARMS RACE DEVELOPENT Theory of Games Strategy & ConflictThe Evolution & Economic Behavior of Cooperation Soviet A-TestThe End of the Cold War Nobel: Harsanyi, Selten & Nash The Evolution of Game Theory A fourth paradigm? EVOLUTIONARY GAMES ?? ESS

“And here it becomes emphatically clear that the intellectual processes of choosing a strategy in pure conflict and choosing a strategy of coordination are of wholly different sorts …. In the pure-coordination game, the player’s objective is to make contact with the other player through some imaginative process of introspection, of searching for shared clues; in the minimax strategy of a zero-sum game … -- one’s whole objective is to avoid any meetings of the mind, even an inadvertent one” (Schelling, 1960, p. 96). The Evolution of Game Theory

Once we move to nonzero-sum games, however, the status of game theory grows ambiguous: Coordination Games Bargaining Games Repeated Games Public Goods Games PLAY BEST RESPONSE STRATEGY? There may be more than one, and the “right” one will depend on what the other/s choose\s. PLAY DOMINANT STRATEGY (when it exists)? PD! Multiple and/or inefficient equilibria

Summary & Conclusion [W]here trust and good faith do not exist and cannot be made to by our acting as though they did, we may wish to solicit advice from the underworld, or from ancient despotism, on how to make agreements when trust and good faith are lacking and there is no legal recourse for breach on contract. The ancient exchanged hostages, drank from the same glass to demonstrate the absence of poison, met in public places (…) and even deliberately exchanged spies to facilitate transmittal of authentic information. It seems likely that a well-developed theory of strategy could (…) discover modern equivalents that, though offensive to our taste, may be desperately needed in the regulation of conflict. – Schelling,1960, p. 20

For Further Interest Binmore, K.Game Theory & the Social Contract, II (1998). Gintis, H.Game Theory Evolving (2000). Kreps, D.Game Theory and Economic Modelling (1994). Raiffa, H.The Art and Science of Negotiation (1982).

Tournament Assignment Design a strategy to play an Evolutionary Prisoner’s Dilemma Tournament. Entries will meet in a round robin tournament, with 1% noise (i.e., for each intended choice there is a 1% chance that the opposite choice will be implemented). Games will last at least 1000 repetitions (each generation), and after each generation, population shares will be adjusted according to the replicator dynamic, so that strategies that do better than average will grow as a share of the population whereas others will be driven to extinction. The winner or winners will be those strategies that survive after at least 10,000 generations.

Tournament Assignment To design your strategy, access the programs through your fas Unix account. The Finite Automaton Creation Tool (fa) will prompt you to create a finite automata to implement your strategy. Select the number of internal states, designate the initial state, define output and transition functions, which together determine how an automaton “behaves.” The program also allows you to specify probabilistic output and transition functions. Simple probabilistic strategies such as GENEROUS TIT FOR TAT have been shown to perform particularly well in noisy environments, because they avoid costly sequences of alternating defections that undermine sustained cooperation.

Preliminary Tournament Results

Problem Set 4.4c

Preliminary Tournament Results

Summary and Conclusions Graduate Paper deadline: Aug 8, by 5pm. Tournament deadline: Aug 10, by 12midnight. Final Exam: Aug 12, 6pm, Sever 214.