A discrete dynamical system for the greedy strategy at collective Parrondo games

We study the emergence of altruistic behaviour in collective games. In particular, we take into account Toral's version of collective Parrondo's paradoxical games, in which the redistribution of capital between agents, who can play different strategies, creates a positive trend of increasing capital. In this framework, we insert two categories of players, altruistic and selfish ones, and see how they interact and how their capital evolves. More in detail, we analyse the positive effects of altruistic behaviour, but we also point out how selfish players take advantage of that situation. The general result is that altruistic behaviour is discouraged, because selfish players get richer while altruistic ones get poorer. We also consider a smarter way of being altruistic, based on reputation, called "selective altruism", which prevents selfish players from taking advantage of altruistic ones. In this new situation it is altruism, and not selfishness, to be encouraged and stabilized. Finally, we introduce a mechanism of imitation between players and study how it influences the composition of the population of both altruistic and selfish players as a function of time for different initial conditions and network topologies adopted.

show abstract

“…There are also collective versions of Parrondo's games that produce paradoxical results [23,24,25,26,27,28]. More specifically, in refs.…”

Section: Parrondo's Paradox In Single and Collective Gamesmentioning

confidence: 99%

“…In other words, game A reduces the number of times that the bad coin is used in game B, making it more profitable. There are also collective versions of Parrondo's games that produce paradoxical results [23,24,25,26,27,28]. More specifically, in refs.…”

Section: Introductionmentioning

confidence: 99%

Selective altruism in collective games

Zappalà

Pluchino

Rapisarda

2014

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

show abstract

“…Since the previous versions have focused on how to modify game B, Toral [9] proposed a modification of game A which is played by N number of players as well. Game A is modified where a player i gives away one unit of his capital to a randomly chosen player j. Ye [10] proposed a multi-agent Parrondo's model based on the network evolution and performed a study of a mechanism depending on the evolution of the network structure (the rewiring mechanism) instead of game A. Ethier [11] has considered a collective version of Parrondo's games with probabilities parametrized by ρ ∈ (0, 1] in which a fraction of an infinite number of players collectively choose and individually play at each turn the game that yields the maximum average profit at that turn. Ye [12] proposed a Parrondo's model based on complex networks, and a structure of game B applied in arbitrary topologies was constructed.…”

Section: Introductionmentioning

confidence: 99%

Random Walks in the Presence of Absorbing Barriers in Parrondo's Games

et al. 2014

View full text Add to dashboard Cite

Communicated by Stefania ResidoriFor a multi-agent spatial Parrondo's model that it is composed of games A and B, we use the discrete time Markov chains to derive the probability transition matrix. Then, we respectively deduce the stationary distribution for games A and B played individually and the randomized combination of game A + B. We notice that under a specific set of parameters, two absorbing states instead of a fixed stationary distribution exist in game B. However, the randomized game A + B can jump out of the absorbing states of game B and has a fixed stationary distribution because of the "agitating" role of game A. Moreover, starting at different initial states, we deduce the probabilities of absorption at the two absorbing barriers.

show abstract

A new theoretical analysis approach for a multi-agent spatial Parrondo’s game

Zheng

et al. 2014

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

A discrete dynamical system for the greedy strategy at collective Parrondo games

Cited by 3 publications

References 15 publications

Selective altruism in collective games

Selective altruism in collective games

Random Walks in the Presence of Absorbing Barriers in Parrondo's Games

A new theoretical analysis approach for a multi-agent spatial Parrondo’s game

Contact Info

Product

Resources

About