39 research outputs found
Defection and extortion as unexpected catalysts of unconditional cooperation in structured populations
We study the evolution of cooperation in the spatial prisoner's dilemma game,
where besides unconditional cooperation and defection, tit-for-tat,
win-stay-lose-shift and extortion are the five competing strategies. While
pairwise imitation fails to sustain unconditional cooperation and extortion
regardless of game parametrization, myopic updating gives rise to the
coexistence of all five strategies if the temptation to defect is sufficiently
large or if the degree distribution of the interaction network is
heterogeneous. This counterintuitive evolutionary outcome emerges as a result
of an unexpected chain of strategy invasions. Firstly, defectors emerge and
coarsen spontaneously among players adopting win-stay-lose-shift. Secondly,
extortioners and players adopting tit-for-tat emerge and spread via neutral
drift among the emerged defectors. And lastly, among the extortioners,
cooperators become viable too. These recurrent evolutionary invasions yield a
five-strategy phase that is stable irrespective of the system size and the
structure of the interaction network, and they reveal the most unexpected
mechanism that stabilizes extortion and cooperation in an evolutionary setting.Comment: 7 two-column pages, 5 figures; accepted for publication in Scientific
Reports [related work available at http://arxiv.org/abs/1401.8294
Comparing reactive and memory-one strategies of direct reciprocity
Direct reciprocity is a mechanism for the evolution of cooperation based on
repeated interactions. When individuals meet repeatedly, they can use
conditional strategies to enforce cooperative outcomes that would not be
feasible in one-shot social dilemmas. Direct reciprocity requires that
individuals keep track of their past interactions and find the right response.
However, there are natural bounds on strategic complexity: Humans find it
difficult to remember past interactions accurately, especially over long
timespans. Given these limitations, it is natural to ask how complex strategies
need to be for cooperation to evolve. Here, we study stochastic evolutionary
game dynamics in finite populations to systematically compare the evolutionary
performance of reactive strategies, which only respond to the co-player's
previous move, and memory-one strategies, which take into account the own and
the co-player's previous move. In both cases, we compare deterministic strategy
and stochastic strategy spaces. For reactive strategies and small costs, we
find that stochasticity benefits cooperation, because it allows for
generous-tit-for-tat. For memory one strategies and small costs, we find that
stochasticity does not increase the propensity for cooperation, because the
deterministic rule of win-stay, lose-shift works best. For memory one
strategies and large costs, however, stochasticity can augment cooperation.Comment: 18 pages, 7 figure
Zero-determinant strategies in finitely repeated games
Direct reciprocity is a mechanism for sustaining mutual cooperation in
repeated social dilemma games, where a player would keep cooperation to avoid
being retaliated by a co-player in the future. So-called zero-determinant (ZD)
strategies enable a player to unilaterally set a linear relationship between
the player's own payoff and the co-player's payoff regardless of the strategy
of the co-player. In the present study, we analytically study zero-determinant
strategies in finitely repeated (two-person) prisoner's dilemma games with a
general payoff matrix. Our results are as follows. First, we present the forms
of solutions that extend the known results for infinitely repeated games (with
a discount factor w of unity) to the case of finitely repeated games (0 < w <
1). Second, for the three most prominent ZD strategies, the equalizers,
extortioners, and generous strategies, we derive the threshold value of w above
which the ZD strategies exist. Third, we show that the only strategies that
enforce a linear relationship between the two players' payoffs are either the
ZD strategies or unconditional strategies, where the latter independently
cooperates with a fixed probability in each round of the game, proving a
conjecture previously made for infinitely repeated games.Comment: 24 pages, 2 figure
Partners or rivals? Strategies for the iterated prisoner's dilemma
Within the class of memory-one strategies for the iterated Prisoner's Dilemma, we characterize partner strategies, competitive strategies and zero-determinant strategies. If a player uses a partner strategy, both players can fairly share the social optimum; but a co-player preferring an unfair solution will be penalized by obtaining a reduced payoff. A player using a competitive strategy never obtains less than the co-player. A player using a zero-determinant strategy unilaterally enforces a linear relation between the two players' payoffs. These properties hold for every strategy used by the co-player, whether memory-one or not
Partners and rivals in direct reciprocity
Reciprocity is a major factor in human social life and accounts for a large part of cooperation in our communities. Direct reciprocity arises when repeated interactions occur between the same individuals. The framework of iterated games formalizes this phenomenon. Despite being introduced more than five decades ago, the concept keeps offering beautiful surprises. Recent theoretical research driven by new mathematical tools has proposed a remarkable dichotomy among the crucial strategies: successful individuals either act as partners or as rivals. Rivals strive for unilateral advantages by applying selfish or extortionate strategies. Partners aim to share the payoff for mutual cooperation, but are ready to fight back when being exploited. Which of these behaviours evolves depends on the environment. Whereas small population sizes and a limited number of rounds favour rivalry, partner strategies are selected when populations are large and relationships stable. Only partners allow for evolution of cooperation, while the rivals’ attempt to put themselves first leads to defection. Hilbe et al. synthesize recent theoretical work on zero-determinant and ‘rival’ versus ‘partner’ strategies in social dilemmas. They describe the environments under which these contrasting selfish or cooperative strategies emerge in evolution
Evolution of direct reciprocity in group-structured populations
People tend to have their social interactions with members of their owncommunity. Such group-structured interactions can have a profound impact on thebehaviors that evolve. Group structure affects the way people cooperate, andhow they reciprocate each other's cooperative actions. Past work has shown thatpopulation structure and reciprocity can both promote the evolution ofcooperation. Yet the impact of these mechanisms has been typically studied inisolation. In this work, we study how the two mechanisms interact. Using agame-theoretic model, we explore how people engage in reciprocal cooperation ingroup-structured populations, compared to well-mixed populations of equal size.To derive analytical results, we focus on two scenarios. In the first scenario,we assume a complete separation of time scales. Mutations are rare compared tobetween-group comparisons, which themselves are rare compared to within-groupcomparisons. In the second scenario, there is a partial separation of timescales, where mutations and between-group comparisons occur at a comparablerate. In both scenarios, we find that the effect of population structuredepends on the benefit of cooperation. When this benefit is small,group-structured populations are more cooperative. But when the benefit islarge, well-mixed populations result in more cooperation. Overall, our resultsreveal how group structure can sometimes enhance and sometimes suppress theevolution of cooperation.<br