Experimental studies of stochastic models for the Prisoner's dilemma

Abstract

A game of strategy represents a situation in which two or more players make choices between available alternatives. When the interests of the players are partly coincident and partly opposed, it is a nonzero‐sum game. The psychologically interesting aspects of this game or of any realistic situation which can be adequately described by it stem from mixed motives, in which the confrontation is not only between the conflicting players but also between the conflicting motives within each player.

Cooperation, but No Reciprocity: Individual Strategies in the Repeated Prisoner’s Dilemma

“…First, I show that the BOS axioms are equivalent to existence of what I propose to call "Semi-Grim" equilibrium, and the Semi-Grim strategy is indeed the puzzling construct σ cc > σ dc = σ cd > σ dd observed by Rapoport and Mowshowitz (1966) and in Table 1. Second, I show in a latent class analysis (the results of which are previewed in Table 1) that the SemiGrim strategy is played by the majority of subjects when it is an equilibrium.…”

“…81, 0.43, 0.37, 0.22) by Rapoport and Mowshowitz (1966), which relates to neither Grim, TFT, nor PTFT, suggested that cooperation between human players is as fuzzy a concept as predicted by Folk theorems (see e.g. Stahl et al, 1991).…”

“…Early experimental work, e.g. Rapoport and Mowshowitz (1966), showed that subjects indeed cooperate, and the results of Axelrod (1980a,b) show that tit-for-tat (TFT) is a theoretically successful strategy in response to opponents with unknown strategies. However, TFT is an not a subgame-perfect equilibrium, and the related "perfect tit-for-tat" (PTFT) strategy (σ cc , σ cd , σ dc , σ dd ) = (1, 0, 0, 1), 1 which tends to be even more effective in response to cooperative strategies (Nowak et al, 1993;Imhof et al, 2007), exists only under the strict condition that one round of punishment suffices to deter defection.…”

“…They analyzed play in a large variety of experimental treatments, and both concluded that the δ -criterion defined axiomatically by BOS is a predictive threshold for cooperation. In addition, the puzzling strategy relation σ cc > σ dc ≈ σ cd > σ dd of Rapoport and Mowshowitz (1966) can be found implicitly in the binary regression models of Bruttel and Kamecke (2012, Table 4), where it obtains for three ways of eliciting strategies (hot play, strategy method, and a Moore Table 1: On average, σ cc > σ dc ≈ σ cd > σ dd obtains in most treatments of four recent experiments, and individually, at least 50% play Semi-Grim in treatments where Semi-Grim MPEs exist (otherwise, the Semi-Grim share is zero). …”

Action learning versus strategy learning

“…Many experiments of this type have been conducted by psychologists since the 1960s and later by experimental economists. In this article, we utilized those done by Rapoport, Guyer, and Gordon [12,henceforth,RGG] and Rapoport and Mowshowitz [13,henceforth,RM].…”