Selfishness, fraternity, and other-regarding preference in spatial evolutionary games

Spatial evolutionary games are studied with myopic players whose payoff interest, as a personal character, is tuned from selfishness to other-regarding preference via fraternity. The players are located on a square lattice and collect income from symmetric two-person two-strategy (called cooperation and defection) games with their nearest neighbors. During the elementary steps of evolution a randomly chosen player modifies her strategy in order to maximize stochastically her utility function composed from her own and the co-players' income with weight factors $1-Q$ and Q. These models are studied within a wide range of payoff parameters using Monte Carlo simulations for noisy strategy updates and by spatial stability analysis in the low noise limit. For fraternal players ($Q=1/2$) the system evolves into ordered arrangements of strategies in the low noise limit in a way providing optimum payoff for the whole society. Dominance of defectors, representing the "tragedy of the commons", is found within the regions of prisoner's dilemma and stag hunt game for selfish players (Q=0). Due to the symmetry in the effective utility function the system exhibits similar behavior even for Q=1 that can be interpreted as the "lovers' dilemma".Comment: 7 two-column pages, 8 figures; accepted for publication in J. Theor. Bio

Imitators and Optimizers in Cournot Oligopoly

We analyze a symmetric n-firm Cournot oligopoly with a heterogeneous population of optimizers and imitators. Imitators mimic the output decision of the most successful firms of the previous round a l`a Vega-Redondo (1997). Optimizers play a myopic best response to the opponents’ previous output. Firms are allowed to make mistakes and deviate from the decision rules with a small probability. Applying stochastic stability analysis, we find that the long run distribution converges to a recurrent set of states in which imitators are better off than are optimizers. This finding appears to be robust even when optimizers are more sophisticated. It suggests that imitators drive optimizers out of the market contradicting a fundamental conjecture by Friedman (1953)

Optimal treatment allocations in space and time for on-line control of an emerging infectious disease

A key component in controlling the spread of an epidemic is deciding where, whenand to whom to apply an intervention.We develop a framework for using data to informthese decisionsin realtime.We formalize a treatment allocation strategy as a sequence of functions, oneper treatment period, that map up-to-date information on the spread of an infectious diseaseto a subset of locations where treatment should be allocated. An optimal allocation strategyoptimizes some cumulative outcome, e.g. the number of uninfected locations, the geographicfootprint of the disease or the cost of the epidemic. Estimation of an optimal allocation strategyfor an emerging infectious disease is challenging because spatial proximity induces interferencebetween locations, the number of possible allocations is exponential in the number oflocations, and because disease dynamics and intervention effectiveness are unknown at outbreak.We derive a Bayesian on-line estimator of the optimal allocation strategy that combinessimulation–optimization with Thompson sampling.The estimator proposed performs favourablyin simulation experiments. This work is motivated by and illustrated using data on the spread ofwhite nose syndrome, which is a highly fatal infectious disease devastating bat populations inNorth America

Imitators and Optimizers in Cournot Oligopoly

We analyze a symmetric n-firm Cournot oligopoly with a heterogeneous population of optimizers and imitators. Imitators mimic the output decision of the most successful firms of the previous round a l`a Vega-Redondo (1997). Optimizers play a myopic best response to the opponents’ previous output. Firms are allowed to make mistakes and deviate from the decision rules with a small probability. Applying stochastic stability analysis, we find that the long run distribution converges to a recurrent set of states in which imitators are better off than are optimizers. This finding appears to be robust even when optimizers are more sophisticated. It suggests that imitators drive optimizers out of the market contradicting a fundamental conjecture by Friedman (1953).profit maximization hypothesis; bounded rationality; learning; Stackelberg

Collective states in social systems with interacting learning agents

We consider a social system of interacting heterogeneous agents with learning abilities, a model close to Random Field Ising Models, where the random field corresponds to the idiosyncratic willingness to pay. Given a fixed price, agents decide repeatedly whether to buy or not a unit of a good, so as to maximize their expected utilities. We show that the equilibrium reached by the system depends on the nature of the information agents use to estimate their expected utilities.Comment: 18 pages, 26 figure

Imitators and Optimizers in Cournot Oligopoly

We present a formal model of symmetric n-firm Cournot oligopoly with a heterogeneous population of profit optimizers and imitators. Imitators mimic the output decision of the most successful firms of the previous round a la Vega-Redondo (1997). Optimizers play myopic best response to the opponents' previous output. The dynamics of the decision rules induce a Markov chain. As expression of bounded rationality, firms are allowed to make mistakes and deviate from the decision rules with a small probability. Applying stochastic stability analysis, we characterize the long run behavior of the oligopoly. We find that the long run distribution converges to a recurrent set of states in which imitators are better off than optimizers. This finding appears to be robust even when optimizers are more sophisticated. It suggests that imitators drive optimizers out of the market contradicting a fundamental conjecture by Friedman (1953).imitation, myopic best reply, bounded rationality, profit maximization hypothesis, stochastic stability, learning, Stackelberg