5,313 research outputs found
Evolutionary stable strategies in networked games: the influence of topology
Evolutionary game theory is used to model the evolution of competing
strategies in a population of players. Evolutionary stability of a strategy is
a dynamic equilibrium, in which any competing mutated strategy would be wiped
out from a population. If a strategy is weak evolutionarily stable, the
competing strategy may manage to survive within the network. Understanding the
network-related factors that affect the evolutionary stability of a strategy
would be critical in making accurate predictions about the behaviour of a
strategy in a real-world strategic decision making environment. In this work,
we evaluate the effect of network topology on the evolutionary stability of a
strategy. We focus on two well-known strategies known as the Zero-determinant
strategy and the Pavlov strategy. Zero-determinant strategies have been shown
to be evolutionarily unstable in a well-mixed population of players. We
identify that the Zero-determinant strategy may survive, and may even dominate
in a population of players connected through a non-homogeneous network. We
introduce the concept of `topological stability' to denote this phenomenon. We
argue that not only the network topology, but also the evolutionary process
applied and the initial distribution of strategies are critical in determining
the evolutionary stability of strategies. Further, we observe that topological
stability could affect other well-known strategies as well, such as the general
cooperator strategy and the cooperator strategy. Our observations suggest that
the variation of evolutionary stability due to topological stability of
strategies may be more prevalent in the social context of strategic evolution,
in comparison to the biological context
Analyzing Social Network Structures in the Iterated Prisoner's Dilemma with Choice and Refusal
The Iterated Prisoner's Dilemma with Choice and Refusal (IPD/CR) is an
extension of the Iterated Prisoner's Dilemma with evolution that allows players
to choose and to refuse their game partners. From individual behaviors,
behavioral population structures emerge. In this report, we examine one
particular IPD/CR environment and document the social network methods used to
identify population behaviors found within this complex adaptive system. In
contrast to the standard homogeneous population of nice cooperators, we have
also found metastable populations of mixed strategies within this environment.
In particular, the social networks of interesting populations and their
evolution are examined.Comment: 37 pages, uuencoded gzip'd Postscript (1.1Mb when gunzip'd) also
available via WWW at http://www.cs.wisc.edu/~smucker/ipd-cr/ipd-cr.htm
On Rational Delegations in Liquid Democracy
Liquid democracy is a proxy voting method where proxies are delegable. We
propose and study a game-theoretic model of liquid democracy to address the
following question: when is it rational for a voter to delegate her vote? We
study the existence of pure-strategy Nash equilibria in this model, and how
group accuracy is affected by them. We complement these theoretical results by
means of agent-based simulations to study the effects of delegations on group's
accuracy on variously structured social networks.Comment: 17 pages, 3 figures. This paper (without Appendix) appears in the
proceedings of AAAI'1
Imitation and Efficient Contagion
In this paper we study the conditions under which efficient behavior can spread from a finite initial seed group to an infinite population living on a network. We formulate conditions on payoffs and network structure under which overall contagion occurs in arbitrary regular networks. Central in this process is the communication pattern among players who are confronted with the same decision, i.e. who are at the same distance from the initial seed group. The extent to which these agents interact among themselves (rather than with players who already have faced or subsequently will face the decision problem) is critical in the Prisoner’s Dilemma. In the Coordination Game the key element is the cohesion of the efficient cluster, a property which is different from the one identified in the Prisoner’s Dilemma. Additional results are obtained when we distinguish the interaction and information neighborhoods. Specifically, we find that contagion tends to be favored by fast neighborhood growth if an assumption of conservative behavior is made. We discuss our findings in relation to the notions of clustering, transitivity and cohesion.imitation, contagion, regular graphs, local interaction game
Defecting or not defecting: how to "read" human behavior during cooperative games by EEG measurements
Understanding the neural mechanisms responsible for human social interactions
is difficult, since the brain activities of two or more individuals have to be
examined simultaneously and correlated with the observed social patterns. We
introduce the concept of hyper-brain network, a connectivity pattern
representing at once the information flow among the cortical regions of a
single brain as well as the relations among the areas of two distinct brains.
Graph analysis of hyper-brain networks constructed from the EEG scanning of 26
couples of individuals playing the Iterated Prisoner's Dilemma reveals the
possibility to predict non-cooperative interactions during the decision-making
phase. The hyper-brain networks of two-defector couples have significantly less
inter-brain links and overall higher modularity - i.e. the tendency to form two
separate subgraphs - than couples playing cooperative or tit-for-tat
strategies. The decision to defect can be "read" in advance by evaluating the
changes of connectivity pattern in the hyper-brain network
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
Learning with Opponent-Learning Awareness
Multi-agent settings are quickly gathering importance in machine learning.
This includes a plethora of recent work on deep multi-agent reinforcement
learning, but also can be extended to hierarchical RL, generative adversarial
networks and decentralised optimisation. In all these settings the presence of
multiple learning agents renders the training problem non-stationary and often
leads to unstable training or undesired final results. We present Learning with
Opponent-Learning Awareness (LOLA), a method in which each agent shapes the
anticipated learning of the other agents in the environment. The LOLA learning
rule includes a term that accounts for the impact of one agent's policy on the
anticipated parameter update of the other agents. Results show that the
encounter of two LOLA agents leads to the emergence of tit-for-tat and
therefore cooperation in the iterated prisoners' dilemma, while independent
learning does not. In this domain, LOLA also receives higher payouts compared
to a naive learner, and is robust against exploitation by higher order
gradient-based methods. Applied to repeated matching pennies, LOLA agents
converge to the Nash equilibrium. In a round robin tournament we show that LOLA
agents successfully shape the learning of a range of multi-agent learning
algorithms from literature, resulting in the highest average returns on the
IPD. We also show that the LOLA update rule can be efficiently calculated using
an extension of the policy gradient estimator, making the method suitable for
model-free RL. The method thus scales to large parameter and input spaces and
nonlinear function approximators. We apply LOLA to a grid world task with an
embedded social dilemma using recurrent policies and opponent modelling. By
explicitly considering the learning of the other agent, LOLA agents learn to
cooperate out of self-interest. The code is at github.com/alshedivat/lola
Oscillatory dynamics in evolutionary games are suppressed by heterogeneous adaptation rates of players
Game dynamics in which three or more strategies are cyclically competitive,
as represented by the rock-scissors-paper game, have attracted practical and
theoretical interests. In evolutionary dynamics, cyclic competition results in
oscillatory dynamics of densities of individual strategists. In finite-size
populations, it is known that oscillations blow up until all but one strategies
are eradicated if without mutation. In the present paper, we formalize
replicator dynamics with players that have different adaptation rates. We show
analytically and numerically that the heterogeneous adaptation rate suppresses
the oscillation amplitude. In social dilemma games with cyclically competing
strategies and homogeneous adaptation rates, altruistic strategies are often
relatively weak and cannot survive in finite-size populations. In such
situations, heterogeneous adaptation rates save coexistence of different
strategies and hence promote altruism. When one strategy dominates the others
without cyclic competition, fast adaptors earn more than slow adaptors. When
not, mixture of fast and slow adaptors stabilizes population dynamics, and slow
adaptation does not imply inefficiency for a player.Comment: 4 figure
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