Combined Problems of Cooperation and Coordination

author: Hans-Ulrich Stark, Chair of Systems Design, ETH Zurich
published: Nov. 28, 2007,   recorded: October 2007,   views: 4652


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In game theory, much attention has been paid to symmetrical 2-players games with binary decisions of the players. Within this frame, questions of social cooperation and social dilemmas have mostly been attached to investigations of the Prisoner's Dilemma (PD) with T > R > P > S and 2R > T + S. In this context, the readiness of individuals to resist the temptation to defect is studied in various settings. These investigations aim at explaining the origin and stability of cooperation among selfish individuals. But what if the readiness to resist temptation is not enough to reach a desired outcome? Maybe there are more than one desired solutions and the individuals additionally have to coordinate their actions to realize one of them. In this work, I focus on game theoretical conflicts that exhibit a combination of cooperation and coordination problems in the same game. Examples are (i) the Turn-Taking Dilemma (Neill, 2003) and (ii) the Route Choice Game (Helbing et al., 2005; Stark et al., 2007). The first one, (i), is similar to the above described PD, but the second inequality is reversed to T + S > 2R. The Pareto-inefficient equilibrium, and, thereby, the cooperation dilemma remains the same, but the system optimal solution (maximal cumulative payoff) is shifted to the off diagonal of the bimatrix. When considering an iterated game, this leads to a non-trivial, temporal coordination problem as flipping between the upper right and the lower left solutions of the bimatrix would lead to the only Pareto-efficient solution of the supergame. The latter point also holds for the Route Choice Game with T > P > S > R and T + S > 2P, that represents the problem of efficient usage of networks with capacity-restricted links (traffic networks, data-communication networks). Of course, investigations regarding the performance of systems with this underlying conflict yield completely different results than those with a PD game underlying. However, currently there is very little work done in this direction. In this contribution, I will present my current research on this topic as well as empirical results of previous work. [1] Helbing, D.; Schönhof, M.; Stark, H.-U.; Holyst, J. A. (2005). How individuals learn to take turns: Emergence of alternating cooperation in a congestion game and the prisoner's dilemma. Adv. Complex Syst. 8, 87-116; [2] Neill, D. B. (2003). Cooperation and coordination in the turn-taking dilemma. In: TARK. pp. 231-244; [3] Stark, H.-U.; Helbing, D.; Schönhof, M.; Holyst, J. A. (2007). Alternating cooperation strategies in a route choice game: Theory, experiments, and effects of a learning scenario. In: A. Innocenti; P. Sbriglia (eds.), Games, Rationality, and Behaviour, Palgrave, MacMillan.

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