Robustness to Strategic Uncertainty (Revision of DP 2010-70)

We model a player’s uncertainty about other players’ strategy choices as smooth probability distributions over their strategy sets. We call a strategy profile (strictly) robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence (all sequences) of strategy profiles, in each of which every player’s strategy is optimal under under his or her uncertainty about the others. We derive general properties of such robustness, and apply the definition to Bertrand competition games and the Nash demand game, games that admit infinitely many Nash equilibria. We show that our robustness criterion selects a unique Nash equilibrium in the Bertrand games, and that this agrees with recent experimental findings. For the Nash demand game, we show that the less uncertain party obtains the bigger share.Nash equilibrium;refinement;strategic uncertainty;price competition;Bertrand competition;bargaining;Nash demand game

Emergence of Cooperation and Organization in an Evolutionary Game

A binary game is introduced and analysed. N players have to choose one of the two sides independently and those on the minority side win. Players uses a finite set of ad hoc strategies to make their decision, based on the past record. The analysing power is limited and can adapt when necessary. Interesting cooperation and competition pattern of the society seem to arise and to be responsive to the payoff function.Comment: 8 pages, 13 figure

Modeling the Evolution of Differences in Variability Between Sexes

An elementary mathematical theory based on a “selectivity-variability” principle is proposed to address a question raised by Charles Darwin, namely, how one sex of a sexually dimorphic species might tend to evolve with greater variability than the other sex. Two mathematical models of the principle are presented: a discrete-time one-step probabilistic model of the short-term behavior of the subpopulations of a given sex, with an example using normally distributed perceived fitness values; and a continuous-time deterministic coupled ODE model for the long-term asymptotic behavior of the expected sizes of the subpopulations, with an example using exponentially distributed fitness levels

Robustness to Strategic Uncertainty (Revision of DP 2010-70)

We model a player’s uncertainty about other players’ strategy choices as smooth probability distributions over their strategy sets. We call a strategy profile (strictly) robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence (all sequences) of strategy profiles, in each of which every player’s strategy is optimal under under his or her uncertainty about the others. We derive general properties of such robustness, and apply the definition to Bertrand competition games and the Nash demand game, games that admit infinitely many Nash equilibria. We show that our robustness criterion selects a unique Nash equilibrium in the Bertrand games, and that this agrees with recent experimental findings. For the Nash demand game, we show that the less uncertain party obtains the bigger share.

Social Dilemmas and Cooperation in Complex Networks

In this paper we extend the investigation of cooperation in some classical evolutionary games on populations were the network of interactions among individuals is of the scale-free type. We show that the update rule, the payoff computation and, to some extent the timing of the operations, have a marked influence on the transient dynamics and on the amount of cooperation that can be established at equilibrium. We also study the dynamical behavior of the populations and their evolutionary stability.Comment: 12 pages, 7 figures. to appea

Evolution of Coordination in Social Networks: A Numerical Study

Coordination games are important to explain efficient and desirable social behavior. Here we study these games by extensive numerical simulation on networked social structures using an evolutionary approach. We show that local network effects may promote selection of efficient equilibria in both pure and general coordination games and may explain social polarization. These results are put into perspective with respect to known theoretical results. The main insight we obtain is that clustering, and especially community structure in social networks has a positive role in promoting socially efficient outcomes.Comment: preprint submitted to IJMP

Experimental analysis of lateral impact on planar brittle material

The fragmentation of alumina and glass plates due to lateral impact is studied. A few hundred plates have been fragmented at different impact velocities and the produced fragments are analyzed. The method employed in this work allows one to investigate some geometrical properties of the fragments, besides the traditional size distribution usually studied in former experiments. We found that, although both materials exhibit qualitative similar fragment size distribution function, their geometrical properties appear to be quite different. A schematic model for two-dimensional fragmentation is also presented and its predictions are compared to our experimental results. The comparison suggests that the analysis of the fragments' geometrical properties constitutes a more stringent test of the theoretical models' assumptions than the size distribution

Selection of noise level in strategy adoption for spatial social dilemmas

We studied spatial Prisoner's Dilemma and Stag Hunt games where both the strategy distribution and the players' individual noise level could evolve to reach higher individual payoff. Players are located on the sites of different two-dimensional lattices and gain their payoff from games with their neighbors by choosing unconditional cooperation or defection. The way of strategy adoption can be characterized by a single $K$ (temperature-like) parameter describing how strongly adoptions depend on the payoff-difference. If we start the system from a random strategy distribution with many different player specific $K$ parameters, the simultaneous evolution of strategies and $K$ parameters drives the system to a final stationary state where only one $K$ value remains. In the coexistence phase of cooperator and defector strategies the surviving $K$ parameter is in good agreement with the noise level that ensures the highest cooperation level if uniform $K$ is supposed for all players. In this paper we give a thorough overview about the properties of this evolutionary process.Comment: 10 two-column pages, 10 figures; accepted for publication in Physical Review

Random replicators with asymmetric couplings

Systems of interacting random replicators are studied using generating functional techniques. While replica analyses of such models are limited to systems with symmetric couplings, dynamical approaches as presented here allow specifically to address cases with asymmetric interactions where there is no Lyapunov function governing the dynamics. We here focus on replicator models with Gaussian couplings of general symmetry between p>=2 species, and discuss how an effective description of the dynamics can be derived in terms of a single-species process. Upon making a fixed point ansatz persistent order parameters in the ergodic stationary states can be extracted from this process, and different types of phase transitions can be identified and related to each other. We discuss the effects of asymmetry in the couplings on the order parameters and the phase behaviour for p=2 and p=3. Numerical simulations verify our theory. For the case of cubic interactions numerical experiments indicate regimes in which only a finite number of species survives, even when the thermodynamic limit is considered.Comment: revised version, removed some mathematical parts, discussion of negatively correlated couplings added, figures adde