Limits...
Zero-Determinant Strategies in Iterated Public Goods Game.

Pan L, Hao D, Rong Z, Zhou T - Sci Rep (2015)

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.

View Article: PubMed Central - PubMed

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.


The upper bounds of χ under different (r, N), when χ > 0.Generally, given a specific multiplication factor r, the upper bound of χ slightly decreases as N increases. A high upper bound of χ is more likely to be realized when r is small, which indicates increasing the reward in a game will restrain the extortion.
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f4: The upper bounds of χ under different (r, N), when χ > 0.Generally, given a specific multiplication factor r, the upper bound of χ slightly decreases as N increases. A high upper bound of χ is more likely to be realized when r is small, which indicates increasing the reward in a game will restrain the extortion.

Mentions: Figure 4 shows the upper bound of χ as a function of the group size N and the multiplication factor r. For a large group size N, it is allowed to set r close to 1 leading to a very large upper bound χ. However, in such a case, due to the small reward induced by r, opponents are usually not willing to cooperate. That is to say, although the effective extortionate ratio can be very large, the payoff under such a severe extortion will be limited. Moreover, substituting the bounds of χ into the probabilistic strategies in equations (12) and (13), we can obtain the allowed range of Φ:


Zero-Determinant Strategies in Iterated Public Goods Game.

Pan L, Hao D, Rong Z, Zhou T - Sci Rep (2015)

The upper bounds of χ under different (r, N), when χ > 0.Generally, given a specific multiplication factor r, the upper bound of χ slightly decreases as N increases. A high upper bound of χ is more likely to be realized when r is small, which indicates increasing the reward in a game will restrain the extortion.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4543983&req=5

f4: The upper bounds of χ under different (r, N), when χ > 0.Generally, given a specific multiplication factor r, the upper bound of χ slightly decreases as N increases. A high upper bound of χ is more likely to be realized when r is small, which indicates increasing the reward in a game will restrain the extortion.
Mentions: Figure 4 shows the upper bound of χ as a function of the group size N and the multiplication factor r. For a large group size N, it is allowed to set r close to 1 leading to a very large upper bound χ. However, in such a case, due to the small reward induced by r, opponents are usually not willing to cooperate. That is to say, although the effective extortionate ratio can be very large, the payoff under such a severe extortion will be limited. Moreover, substituting the bounds of χ into the probabilistic strategies in equations (12) and (13), we can obtain the allowed range of Φ:

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.

View Article: PubMed Central - PubMed

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.