Stability of Strict Equilibria in Best Experienced Payoff Dynamics: Simple Formulas and Applications

We consider a family of population game dynamics known as Best Experienced Payoff Dynamics. Under these dynamics, when agents are given the opportunity to revise their strategy, they test some of their possible strategies a fixed number of times. Crucially, each strategy is tested against a new randomly drawn set of opponents. The revising agent then chooses the strategy whose total payoff was highest in the test, breaking ties according to a given tie-breaking rule. Strict Nash equilibria are rest points of these dynamics, but need not be stable. We provide some simple formulas and algorithms to determine the stability or instability of strict Nash equilibria.Spanish State Research Agency (PID2020-118906GB-I00/AEI/10.13039/501100011033), from the Spanish Ministry of Science, Innovation and Universities (PRX19/00113, PRX21/00295), and from the Fulbright Program (PRX19/00113, PRX21/00295), is gratefully acknowledged. Luis R. Izquierdo is grateful to the Center for Control, Dynamical Systems, and Computation at UC Santa Barbara, where part of this work was done, for their hospitality

"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

Strictly Dominated Strategies in the Replicator-Mutator Dynamics

The replicator-mutator dynamics is a set of differential equations frequently used in biological and socioeconomic contexts to model evolutionary processes subject to mutation, error or experimentation. The replicator-mutator dynamics generalizes the widely used replicator dynamics, which appears in this framework as the extreme case where replication is perfectly precise. This paper studies the influence of strictly dominated strategies on the location of the rest points of the replicator-mutator dynamics, at the limit where the mutation terms become arbitrarily small. It can be proved that such limit rest points for small mutation are Nash equilibria, so strictly dominated strategies do not occur at limit stationary points. However, we show through a simple case how strictly dominated strategies can have an influence on the location of the limit rest points for small mutation. Consequently, the characterization of the limit rest points of the replicator-mutator dynamics cannot in general proceed safely by readily eliminating strictly dominated strategiesJCyL (GREX251-2009 and VA006B09), Ministry of Science and Innovation (TIN2008-06464-C03-02, DPI2010-16920 and CSD2010-00034), Ministry of Education (grant JC2009-00263

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

EvoDyn-3s: A Mathematica computable document to analyze evolutionary dynamics in 3-strategy games

EvoDyn-3s generates phase portraits of evolutionary dynamics, as well as data for the analysis of their equilibria. The considered evolutionary dynamics are ordinary differential equations based on adaptive processes taking place in a population of players who are randomly and repeatedly matched in couples to play a 2-player symmetric normal-form game with three strategies. EvoDyn-3s calculates the rest points of the dynamics using exact arithmetic, and represents them. It also provides the eigenvalues of the Jacobian of the dynamics at the isolated rest points, which are useful to evaluate their local stability. The user only needs to specify the 3 × 3 payoff matrix of the game and choose the dynamics.Spanish Ministry of Science and Innovation ’s project ECO2017-83147-C2-2-P (MINECO/AEI/FEDER, UE

Stability for best experienced payoff dynamics

We study a family of population game dynamics under which each revising agent randomly selects a set of strategies according to a given test-set rule; tests each strategy in this set 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, breaking ties according to a given tie-breaking rule. These dynamics need not respect dominance and related properties except as the number of trials become large. Strict Nash equilibria are rest points but need not be stable. We provide a variety of sufficient conditions for stability and for instability, and illustrate their use through a range of applications from the literature

Innovation, catch-up, and leadership in science-based industries

In this article, we seek to shed new light on the sources of industrial leadership and catch-up in science-based industries. We propose an evolutionary model that incorporates scientists’ training and migration, endogenous R&D decisions, and the possibility of funding capital accumulation through debt. The analysis of the model allows us to characterize a robust pattern of industrial catch-up. Likewise, the sensitivity analysis shows which parameters act as pro-catch-up factors or slow down the process. The identification of stationary-state conditions of the model helps us to interpret the simulations, and highlights crucial interactions between technology-supporting institutions and market demand at the basis of industrial catch-up. Finally, the robustness analysis reveals further interdependencies among innovation, scientist mobility, and demandMinisterio de Ciencia e Innovación (project ECO2010-14929)This is a pre-copyedited, author-produced PDF of an article accepted for publication in Industrial and Corporate Change following peer review. The version of record Isabel Almudi, Francisco Fatas-Villafranca, and Luis R. Izquierdo Innovation, catch-up, and leadership in science-based industries Ind Corp Change (2012) 21 (2): 345-375 doi:10.1093/icc/dtr041, is available online at: http://icc.oxfordjournals.org/content/21/2.to

Industry dynamics, technological regimes and the role of demand

In this paper, we propose an industrial dynamics model to analyze the interactions between the price-performance sensitivity of demand, the sources of innovation in a sector, and certain features of the corresponding pattern of industrial transformation. More precisely, we study market concentration in different technological regimes and demand conditions. The computational analysis of our model shows that market demand plays a key role in industrial dynamics. Thus, although for intermediate values of the price-performance sensitivity, our results show the well-known relationships in the literature between technological regimes and industry transformation, we find surprising outcomes when demand is strongly biased either towards price or performance. Hence, for different technological regimes, a high performance sensitivity of demand tends to concentrate the market. On the other hand, under conditions of high price sensitivity, the industry generally tends to atomize. That is to say, for extreme values of the price-performance sensitivity of demand, we find concentrated or atomized market structures no matter the technological regime we are in. These results highlight the importance of considering the role of demand in the analysis of industrial dynamics

Mixing and diffusion in a two-type population

The outbreak of epidemics, the rise of religious radicalization or the motivational influence of fellow students in classrooms are some of the issues that can be described as diffusion processes in heterogeneous groups. Understanding the role that interaction patterns between groups (e.g. homophily or segregation) play in the diffusion of certain traits or behaviours is a major challenge for contemporary societies. Here, we study the impact on diffusion processes of mixing (or, alternatively, segregating) two groups that present different sensitivities or propensities to contagion. We find non-monotonic effects of mixing and inefficient segregation levels, i.e. situations where a change in the mixing level can benefit both groups, e.g. where an increase in the mixing level can reduce the expected contagion levels in both groups. These findings can have fundamental consequences for the design of inclusion policies.D.L.-P. from the Spanish Ministry of Science and Innovation (ECO2011-22919) and from project ECO2017-83147-C2-1-P (MINECO/AEI/FEDER, UE). L.R.I. and S.S.I. from project ECO2017-83147-C2-2-P (MINECO/AEI/FEDER, UE

Artificial economics: a critical review

La economía artificial es uno de los métodos o enfoques de investigación para el estudio de sistemas socioeconómicos complejos con mayor crecimiento durante los últimos años. Este artículo presenta una visión crítica sobre sus características, su potencial y los riesgos relativos al uso de esta metodología. Para ello, encontramos útil relacionar y comparar a la economía artificial con la economía teórica más tradicional. Desde nuestro análisis, la economía teórica y la economía artificial comparten los mismos objetivos, presentan menos diferencias metodológicas de las que a primera vista pudiera parecer, y sus aproximaciones son sin duda complementarias.Artificial Economics is one of the fastest growing approaches to analyse complex socio-economic systems. In this paper we present our views on the distinguishing features of Artificial Economics and on its relation with Theoretical Economics — the field that in our opinion lies closest to Artificial Economics. In this context, we discuss various reasons why conducting research on Artificial Economics may be worthwhile, and provide general guidelines on how to go about it. Our view is that Artificial Economics and Theoretical Economics share the same goals, do not differ conceptually as much as it is sometimes perceived, and their approaches are certainly complementary.Ministerio de Ciencia e Innovación del Reino de España a través del proyecto CSD2010-00034 (SIMULPAST)