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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.


Illustration of the three-player repeated game.(a) For a previous outcome CDD, the conditional probabilities that the player 1, 2 and 3 select C in the current round are ,  and , respectively. Therefore, the probability of transiting from the previous state  to the current state CDD is . (b) The strategies and payoff vectors for the three-player IPGG. (c) After some elementary column operations on matrix M-I, the dot product of an arbitrary vector u with the stationary vector  is equal to the determinant det(p1, p2, p3, u), in which the fourth, sixth and seventh columns ,  and  are only controlled by the players 1, 2 and 3, respectively.
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f1: Illustration of the three-player repeated game.(a) For a previous outcome CDD, the conditional probabilities that the player 1, 2 and 3 select C in the current round are , and , respectively. Therefore, the probability of transiting from the previous state to the current state CDD is . (b) The strategies and payoff vectors for the three-player IPGG. (c) After some elementary column operations on matrix M-I, the dot product of an arbitrary vector u with the stationary vector is equal to the determinant det(p1, p2, p3, u), in which the fourth, sixth and seventh columns , and are only controlled by the players 1, 2 and 3, respectively.

Mentions: where represents the cooperating probability in the current round conditioning on the i-th outcome of the previous round. Figure 1(a,b) depict an example for a three-player repeated game, in which the possible outcomes are {CCC,CCD,CDC,CDD,DCC,DCD,DDC,DDD}.


Zero-Determinant Strategies in Iterated Public Goods Game.

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

Illustration of the three-player repeated game.(a) For a previous outcome CDD, the conditional probabilities that the player 1, 2 and 3 select C in the current round are ,  and , respectively. Therefore, the probability of transiting from the previous state  to the current state CDD is . (b) The strategies and payoff vectors for the three-player IPGG. (c) After some elementary column operations on matrix M-I, the dot product of an arbitrary vector u with the stationary vector  is equal to the determinant det(p1, p2, p3, u), in which the fourth, sixth and seventh columns ,  and  are only controlled by the players 1, 2 and 3, respectively.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f1: Illustration of the three-player repeated game.(a) For a previous outcome CDD, the conditional probabilities that the player 1, 2 and 3 select C in the current round are , and , respectively. Therefore, the probability of transiting from the previous state to the current state CDD is . (b) The strategies and payoff vectors for the three-player IPGG. (c) After some elementary column operations on matrix M-I, the dot product of an arbitrary vector u with the stationary vector is equal to the determinant det(p1, p2, p3, u), in which the fourth, sixth and seventh columns , and are only controlled by the players 1, 2 and 3, respectively.
Mentions: where represents the cooperating probability in the current round conditioning on the i-th outcome of the previous round. Figure 1(a,b) depict an example for a three-player repeated game, in which the possible outcomes are {CCC,CCD,CDC,CDD,DCC,DCD,DDC,DDD}.

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.