Exploring the cooperative regimes in an agent-based model: indirect reciprocity vs. selfish incentives
Authored by H Fort
Date Published: 2003-08-01
DOI: 10.1016/s0378-4371(03)00263-2
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Abstract
The self-organization in cooperative regimes in a simple mean-field version of a model based on “selfish” agents which play the Prisoner's Dilemma (PD) game is studied. The agents have no memory and use strategies not based on direct reciprocity nor “tags”. Two variables are assigned to each agent k at time t, measuring its capital C(k; t) and its probability of cooperation p(k; t). At each time step t a pair of agents interact by playing the PD game. These two agents update their probability of cooperation p(k; t) as follows: they compare the profits they made in this interaction deltaC(k; t) with an estimator epsilon(k; t) and, if deltaC(k; t) greater than or equal to epsilon(k; t), agent i increases its p(k; t) while if deltaC(k; t) < ε(k; t) the agent decreases p(k; t). The 4! = 24 different cases produced by permuting the four Prisoner's Dilemma canonical payoffs 3, 0, 1, and 5-corresponding, respectively, to R (reward), S (sucker's payoff), T (temptation to defect) and P (punishment)-are analyzed. It turns out that for all these 24 possibilities, after a transient, the system self-organizes into a stationary state with average equilibrium probability of cooperation <(p)over bar>(infinity) = constant > 0. Depending on the payoff matrix, there are different equilibrium states characterized by their average probability of cooperation and average equilibrium per capita income ((p) over bar (infinity), delta(C) over bar (infinity)). (C) 2003 Elsevier B.V. All rights reserved.
Tags
Agent-based models
Complex adaptive systems
social systems