The agencies method for coalition formation in experimental games

Abstract

In society, power is often transferred to another person or group. A previous work studied the evolution of cooperation among robot players through a coalition formation game with a noncooperative procedure of acceptance of an agency of another player. Motivated by this previous work, we conduct a laboratory experiment on finitely repeated three-person coalition formation games. Human players with different strength according to the coalition payoffs can accept a transfer of power to another player, the agent, who then distributes the coalition payoffs. We find that the agencies method for coalition formation is quite successful in promoting efficiency. However, the agent faces a tension between short-term incentives of not equally distributing the coalition payoff and the long-term concern to keep cooperation going. In a given round, the strong player in our experiment often resolves this tension approximately in line with the Shapley value and the nucleolus. Yet aggregated over all rounds, the payoff differences between players are rather small, and the equal division of payoffs predicts about 80% of all groups best. One reason is that the voting procedure appears to induce a balance of power, independent of the individual player's strength: Selfish subjects tend to be voted out of their agency and are further disciplined by reciprocal behaviors.leader | rules | reciprocity | fairness T he evolution of human altruism and cooperation is a puzzle. Unlike other animals, people frequently cooperate even absent of any material or reputational incentive to do so. In this paper we show how a voting procedure to transfer power to another person successfully promotes cooperation by balancing the tension between short-term incentives to defect and long-term incentives to keep cooperation going. Our work is inspired by John Nash (1), who theoretically studied the evolution of cooperation among robot players through acceptance of an agency of another player.Beyond Nash's (1) work, there is virtually no work on the agencies method in (experimental) economics as we apply it in our paper. The underlying idea is simple and important: Human subjects can transfer the power to an agency, who determines the final payoff distribution within the group.* Our game reflects that, often, efficiency requires people's willingness to accept the agency of others, such as political, social, or economic leaders (for voting of an expert, see ref. 7).In Nash's (1) work, the robots employed optimal strategies, being the computational result of complex systems of equations. Motivated by Nash's paper, we study laboratory three-person coalition formation games with a non-cooperative procedure of acceptance of an agency of another player. The base games are finitely repeated for 40 rounds with the same three subjects, allowing cooperation and coordination to evolve. In our games non-cooperative game theory cannot organize behavior because it is basically consistent with any outcome. Thus, even the strategies of fully rational agents cannot be predi...

Delegation and Public Pressure in a Threshold Public Goods Game: Theory and Experimental Evidence

“…In a voluntary contribution fundraising exercise, Kumru and Vesterlund (2010) find that donations from individuals with higher social rank increase subsequent contributions. Then, Nash et al (2012) find that delegating the coalition payoffs distribution to an elected agent increases the efficiency and the equality of payoffs in a coalition formation game.…”

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“…More recently, Nash et al [22] conducted an experiment to test a bargaining coalition formation game where players form coalitions by transferring bargaining rights to another player (the "agent"), who is then tasked to distribute payoffs to the coalition. While this paper highlights the tension between the incentive of players to keep a larger share of the resource and maintaining cooperation inside the coalition, it does not address the issue of dynamic coalition stability and the tension between myopic and farsighted payoffs.…”

“…This behavior may be consistent with both empirical expected pay-off maximization and farsighted behavior. 22 Figure 5 shows how these responses evolve throughout the games. 23 For an agent with drawn power 20, the proportion of rejecting two-person coalitions increases throughout the games and at the same time the proportion of accepting the grand coalition also increases (see the logit model in Table A6 in Appendix C).…”

Myopic and farsighted stability in network formation games: an experimental study

“…For example, networks that are pairwise (myopically) stable according to Jackson and Wolinsky (1996) are justified as being stable because any deviation would incur an immediate cost, and networks that are farsightedly stable are such because chains of deviations may incur costs. A further reason for using cooperative concepts in a repeated payoff environment is given by Nash et al (2012) who follow the same approach for a repeated multilateral bargaining game: in their game, as in ours, almost any outcome can be supported as a subgame-perfect Nash equilibrium, so cooperative theories are required to make useful predictions. 8 Other recent papers using a similar methodology include Berninghaus et al (2006), Burger and Buskens (2009), Tremewan andVanberg (2016), andVan Dolder andBuskens (2014).…”