Monte Carlo Strategies for Exploiting Fairness in N-Player Ultimatum Games

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2019 IEEE Conference on Games (cog)

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The Ultimatum Game (UG) is studied to see how people respond in bargaining situations. In the 2-player version each round a player can be a proposer or a responder. As a proposer an offer is made on how to split a monetary amount. The responder either accepts or rejects the offer. If accepted, the money is split as proposed; if rejected both players get nothing. Studies have found over time the offers decrease but are still accepted (getting something is better than nothing) until a subgame perfect Nash equilibrium is reached where the lowest possible offer is accepted. In the N-player version the object is to see if the population can reach a state of fairness where, on average, offers are accepted. We have previously shown that a (μ/μ,λ) evolution strategy can evolve offers and acceptance thresholds that promote fairness. In this paper we report an extension to this previous work. One player is added to the population who interacts in the same manner with the other N players. However, this new player is rational-i.e., he ignores fairness and instead exploits the other players by maximizing his payoffs. We used three different versions of Monte Carlo Tree Search (MCTS) to adaptively control this rational player's offer levels during the game. The results indicate payoffs for this player can be as much as 40% higher than the population average payoff. Our MCTS introduces a novel rollout approach making it ideally suited for the play of mathematical games.



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