Zero-Determinant Strategies in Iterated Public Goods Game.
Bottom Line:
A player adopting zero-determinant strategies is able to pin the expected payoff of the opponents or to enforce a linear relationship between his own payoff and the opponents' payoff, in a unilateral way.This paper considers zero-determinant strategies in the iterated public goods game, a representative multi-player game where in each round each player will choose whether or not to put his tokens into a public pot, and the tokens in this pot are multiplied by a factor larger than one and then evenly divided among all players.The analytical and numerical results exhibit a similar yet different scenario to the case of two-player games: (i) with small number of players or a small multiplication factor, a player is able to unilaterally pin the expected total payoff of all other players; (ii) a player is able to set the ratio between his payoff and the total payoff of all other players, but this ratio is limited by an upper bound if the multiplication factor exceeds a threshold that depends on the number of players.
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Affiliation: CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, China.
ABSTRACT
Recently, Press and Dyson have proposed a new class of probabilistic and conditional strategies for the two-player iterated Prisoner's Dilemma, so-called zero-determinant strategies. A player adopting zero-determinant strategies is able to pin the expected payoff of the opponents or to enforce a linear relationship between his own payoff and the opponents' payoff, in a unilateral way. This paper considers zero-determinant strategies in the iterated public goods game, a representative multi-player game where in each round each player will choose whether or not to put his tokens into a public pot, and the tokens in this pot are multiplied by a factor larger than one and then evenly divided among all players. The analytical and numerical results exhibit a similar yet different scenario to the case of two-player games: (i) with small number of players or a small multiplication factor, a player is able to unilaterally pin the expected total payoff of all other players; (ii) a player is able to set the ratio between his payoff and the total payoff of all other players, but this ratio is limited by an upper bound if the multiplication factor exceeds a threshold that depends on the number of players. No MeSH data available. Related in: MedlinePlus |
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Mentions: where denotes the relation between pC,N−1 and pD,0. The opponents’ total payoff thus depends on the number of players N, the multiplication factor r and the parameter γ. Player 1 can thus adjust the opponents’ total payoff by adopting strategies that results in different values of γ. Note that the same equalizer effect can be realized by different equalizer strategies with the same γ. Figure 2 shows the relationship between player 1’s payoff and the other two players’ average payoff in a three-player IPGG, when player 1 adopts non-ZD and ZD strategies while his opponents adopt random strategies. Under different equalizer strategies, the average payoff of the opponents varies. By inspection on equation (10), a large pC,N−1 or a small pD,0 brings a small γ, and consequently increases the total payoff of the opponents. The range of possible total payoff of the opponents is also strongly affected by r and N: (i) when , player can set this value from (N − 1) to r(N − 1), or equivalently, he can set the average payoff of co-players from 1 to r; (ii) when , the feasible region shrinks as the increase of r; and (iii) when , player can only fix the opponents’ total payoff to (see more detail in Supplementary Methods). |
View Article: PubMed Central - PubMed
Affiliation: CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, China.
No MeSH data available.