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Exploiter, leader, hero, and martyr: The four archetypes of the 2 × 2 game
Author(s) -
Rapoport Anatol
Publication year - 1967
Publication title -
behavioral science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 45
eISSN - 1099-1743
pISSN - 0005-7940
DOI - 10.1002/bs.3830120202
Subject(s) - outcome (game theory) , repeated game , archetype , simultaneous game , symmetric game , hero , mathematical economics , stochastic game , normal form game , strategy , psychology , social psychology , computer science , game theory , economics , philosophy , artificial intelligence , theology
If the payoffs of a 2 × 2 game (two players, each with a choice of two strategies) are defined only on an ordinal scale, there are exactly 78 nonequivalent games of this sort. Of these, twelve are symmetric; that is, in these games each of the players has the same payoff matrix. Of the twelve symmetric games, eight are trivial, in the sense that the same outcome is the most preferred by both players, so that there is no conflict of interest. The remaining four games bring out four distinct types of “psychological pressure” operating on each player. These pressures are seen as the motivations of a player to shift from the so‐called natural (minimax) outcome of the game. In three of the games the motivation to shift is governed by a greater payoff which accrues to the shifting player (if he shifts alone). These, in turn, make the shifting player either an “exploiter” (because he is rewarded but the other is punished), or a “leader” (because both are rewarded but the shifting player more than the other), or a “hero” (because both are rewarded, but the shifting player less than the other). In each of these three games there is also a counterpressure against shifting, because if both shift, both lose. In the fourth game, on the contrary, the immediate pressure is against shifting away from the natural outcome, because the shifting player punishes himself while rewarding the other, that is, becomes a “martyr.” But there is also a counterpressure to shift, because if both shift, both gain. This game is known as Prisoner's Dilemma.