Games with Small Forgetfulness

While it is known how players may learn to play in a game they know, the issue of how their model of the game evolves over time is largely unexplored. This paper introduces small forgetfulness and shows that it may destabilize standard full-memory solutions. Players are repeatedly matched to play a game. After any match, they forget with infinitesimal probability the feasibility of any opponents' unobserved action, and they are reminded of all actions that they observe. During each period, they play an equilibrium consistent with their perception of the game. We show that the unique backward induction path drifts into a non-Nash, self-confirming equilibrium, in a class of extensive-form games that are fully characterized. Such a long-run prediction is always Pareto-undominated, and may Pareto dominate the original backward induction path. In one-shot simultaneous-move games, forgetfulness yields a refinement stronger than trembling hand perfection. Our results imply that there are games that players may never fully learn.

Drift effect and timing without observability: experimental evidence

We provide experimental evidence to Binmore and Samuelson’s (1999) insights for modeling the learning process through which equilibrium is selected. They proposed the concept of drift to describe the effect of perturbations on the dynamic process leading to equilibrium in evolutionary games with boundedly rational agents. We test within a random matched population two different versions of the Dalek game where the forward induction equilibrium weakly iterately dominates the other Nash equilibrium in pure strategies. We also assume that the first mover makes her decision first (“timing”) but the second mover is not informed of the first mover's choice (“lack of observability”). Both players are informed of their position in the sequence and of the fact that the second player will decide without knowing the decision of the first player. If the actual observed choices are only those made by other players in previous interactions, the role played by forward induction is replaced with the learning process taking place within the population. Our results support Binmore and Samuelson’s model because the frequency of the forward induction outcome is payoff-sensitive: it strongly increases when we impose a slight change in the payoffs that does not change equilibrium predictions. This evidence reinforces the evolutionary nature of the drift effect.evolutionary games, experiments, drift, forward induction, order of play. J.E.L. Classification: C72, C91

Best experienced payoff dynamics and cooperation in the centipede game

We study population game dynamics under which each revising agent tests each of his strategies a fixed number of times, with each play of each strategy being against a newly drawn opponent, and chooses the strategy whose total payoff was highest. In the centipede game, these best experienced payoff dynamics lead to cooperative play. When strategies are tested once, play at the almost globally stable state is concentrated on the last few nodes of the game, with the proportions of agents playing each strategy being largely independent of the length of the game. Testing strategies many times leads to cyclical play.U.S. National Science Foundation (Grants SES-1458992 and SES- 1728853), the U.S. Army Research Office (Grants W911NF-17-1-0134 MSN201957), Project ECO2017-83147- C2-2-P (MINECO/AEI/FEDER, UE), and the Spanish Ministerio de Educación, Cultura, y Deporte (Grants PRX15/00362 and PRX16/00048

"Test two, choose the better" leads to high cooperation in the Centipede game

Explaining cooperative experimental evidence in the Centipede game constitutes a challenge for rational game theory. Traditional analyses of Centipede based on backward induction predict uncooperative behavior. Furthermore, analyses based on learning or adaptation under the assumption that those strategies that are more successful in a population tend to spread at a higher rate usually make the same prediction. In this paper we consider an adaptation model in which agents in a finite population do adopt those strategies that turn out to be most successful, according to their own experience. However, this behavior leads to an equilibrium with high levels of cooperation and whose qualitative features are consistent with experimental evidence.Financial support from the Spanish State Research Agency (PID2020-118906GB-I00 / AEI / 10.13039/501100011033), from “Junta de Castilla y León - Consejería de Educación” through BDNS 425389, from the Spanish Ministry of Science, Innovation and Universities (PRX18-00182, PRX19/00113), and from the Fulbright Program (PRX19/00113), is gratefully acknowledged

Kinetic approaches to lactose operon induction and bimodality

The quasi-equilibrium approximation is acceptable when molecular interactions are fast enough compared to circuit dynamics, but is no longer allowed when cellular activities are governed by rare events. A typical example is the lactose operon (lac), one of the most famous paradigms of transcription regulation, for which several theories still coexist to describe its behaviors. The lac system is generally analyzed by using equilibrium constants, contradicting single-event hypotheses long suggested by Novick and Weiner (1957). Enzyme induction as an all-or-none phenomenon. Proc. Natl. Acad. Sci. USA 43, 553-566) and recently refined in the study of (Choi et al., 2008. A stochastic single-molecule event triggers phenotype switching of a bacterial cell. Science 322, 442-446). In the present report, a lac repressor (LacI)-mediated DNA immunoprecipitation experiment reveals that the natural LacI-lac DNA complex built in vivo is extremely tight and long-lived compared to the time scale of lac expression dynamics, which could functionally disconnect the abortive expression bursts and forbid using the standard modes of lac bistability. As alternatives, purely kinetic mechanisms are examined for their capacity to restrict induction through: (i) widely scattered derepression related to the arrival time variance of a predominantly backward asymmetric random walk and (ii) an induction threshold arising in a single window of derepression without recourse to nonlinear multimeric binding and Hill functions. Considering the complete disengagement of the lac repressor from the lac promoter as the probabilistic consequence of a transient stepwise mechanism, is sufficient to explain the sigmoidal lac responses as functions of time and of inducer concentration. This sigmoidal shape can be misleadingly interpreted as a phenomenon of equilibrium cooperativity classically used to explain bistability, but which has been reported to be weak in this system

Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure

Evaluating Competition Strategies for Generic Drug Industries Using Game Theory - A supplement to report “Scenario Planning as a Tool for Long Term Strategic Planning”

This report is a supplement to the project titled “Scenario Planning as a Tool for Long Term Strategic Planning - The Generics Drug Industry in the European Union.” The report will further evaluate the resultant scenarios and strategies build and recommended as part of the titled project mentioned above. Game theory perspectives will be used as a tool to analyse how economic agents (stakeholders of the pharmaceutical generic drugs industry) will react when what they do affects the actions of others. The report will evaluate hypothetical actions taken by generic drugs industry players and their outcomes/payoffs relative to the competitions. It will draw on strategic and extensive forms of games to identify how to act and how to think about your rival’s actions. What would be a more powerful in business strategy than this

Carrot or Stick? Group Selection and the Evolution of Reciprocal Preferences

This paper studies the evolution of both characteristics of reciprocity - the willingness to reward friendly behavior and the willingness to punish hostile behavior. Firstly, preferences for rewarding as well as preferences for punishing can survive evolution provided individuals interact within separated groups. This holds even with randomly formed groups and even when individual preferences are unobservable. Secondly, preferences for rewarding survive only in coexistence with self-interested preferences. But preferences for punishing tend either to vanish or to dominate the population entirely. Finally, the evolution of preferences for rewarding and the evolution of preferences for punishing influence each other decisively. The existence of rewarders enhances the evolutionary success of punishers, but punishers crowd out rewarders