Best reply structure and equilibrium convergence in generic games

Pangallo, Marco; Heinrich, Torsten; Farmer, J. Doyne

doi:10.1126/sciadv.aat1328

Cited by 28 publications

(14 citation statements)

References 58 publications

(76 reference statements)

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“…Note that the above sequential best response algorithm does not ensure that all Nash equilibria of the game are found. Indeed, cycles of best response are widely observed in generic two-player dynamic games [62]. For adaptive agents studied below, there is no limit cycle due to the existence of global maxima of the payoff functions.…”

Section: Best Responses and Emergent Prisoner's Dilemma 441 Best Resp...mentioning

confidence: 96%

Thermodynamic selection: mechanisms and scenarios

2022

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Thermodynamic selection is an indirect competition between agents feeding on the same energy resource and obeying the laws of thermodynamics. We examine scenarios of this selection, where the agent is modeled as a heat-engine coupled to two thermal baths and extracting work from the high-temperature bath. The agents can apply different work-extracting, game-theoretical strategies, e.g. the maximum power or the maximum efficiency. They can also have a fixed structure or be adaptive. Depending on whether the resource (i.e. the high-temperature bath) is infinite or finite, the fitness of the agent relates to the work-power or the total extracted work. These two selection scenarios lead to increasing or decreasing efficiencies of the work-extraction, respectively. The scenarios are illustrated via plant competition for sunlight, and the competition between different ATP production pathways. We also show that certain general concepts of game-theory and ecology--the prisoner's dilemma and the maximal power principle--emerge from the thermodynamics of competing agents. We emphasize the role of adaptation in developing efficient work-extraction mechanisms.

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Section: Best Responses and Emergent Prisoner's Dilemma 441 Best Resp...mentioning

confidence: 96%

Thermodynamic selection: mechanisms and scenarios

2022

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“…Moreover, in this framework we can recover known general results on behavioral economics, as specific games created and played in society (Kahneman et al 1986;Nowak et al 2000;Pangallo et al 2019). For an informal introduction to game theory in diverse branches of philosophy we refer to De Bruin (2005).…”

Section: Governance Markets and Wealthmentioning

confidence: 99%

A Fair Governance: On Inequality, Power and Democracy

Barucca

2020

Topoi

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Can governments keep the pace of global markets? It is a defining characteristic of the present times, tested and measured within multiple studies, that we are living in an increasingly interconnected economy in which giant companies emerge and compete presenting new goods and products at a global scale. The competing environment of international markets produces quickly growing creatures that old nation-states struggle to understand, monitor and, consequently, regulate. In this regard, the selection process taking place in the market seems to be far more effective and greedy than the selection process we apply to our governments. In this paper I discuss the basic theoretical mechanisms for the persistence of wealth concentration, introducing a general game-theoretical framework to connect governance, market economy, and wealth distribution, and to rethink democracy and fairness in policy-making, especially with the aim of global sustainability governance.

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“…According to the static analysis performed in the previous Section, all pure Nash equilibria can be at least in principle achieved as fixed points of the deterministic best-response dynamics. As evidenced by the identified threshold condition for global contagion [71,104,122,169], Nash equilibria have instead rather different basins of attraction, whose properties are very difficult to study analytically and even computationally [136]. We refer to App.…”

Section: Dynamical Equilibrium Selectionmentioning

confidence: 99%

Coordination problems on networks revisited: statics and dynamics

Dall'Asta

2021

Preprint

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Simple binary-state coordination models are widely used to study collective socio-economic phenomena such as the spread of innovations or the adoption of products on social networks. The common trait of these systems is the occurrence of large-scale coordination events taking place abruptly, in the form of a cascade process, as a consequence of small perturbations of an apparently stable state. The conditions for the occurrence of cascade instabilities have been largely analysed in the literature, however for the same coordination models no sufficient attention was given to the relation between structural properties of (Nash) equilibria and possible outcomes of dynamical equilibrium selection. Using methods from the statistical physics of disordered systems, the present work investigates both analytically and numerically, the statistical properties of such Nash equilibria on networks, focusing mostly on random graphs. We provide an accurate description of these properties, which is then exploited to shed light on the mechanisms behind the onset of coordination/miscoordination on large networks. This is done studying the most common processes of dynamical equilibrium selection, such as best response, bounded-rational dynamics and learning processes. In particular, we show that well beyond the instability region, full coordination is still globally stochastically stable, however equilibrium selection processes with low stochasticity (e.g. best response) or strong memory effects (e.g. reinforcement learning) can be prevented from achieving full coordination by being trapped into a large (exponentially in number of agents) set of locally stable Nash equilibria at low/medium coordination (inefficient equilibria). These results should be useful to allow a better understanding of general coordination problems on complex networks. CONTENTS I. IntroductionII. A coordination model with heterogeneous payoffs III. Monotone decision processes A. Message-passing equations for minimal equilibria and global cascade condition B. Properties of the maximal equilibria IV. The equilibrium landscape A. Cavity method for Nash equilibria B. Results for random regular graphs C. Results on non-regular random graphs V. Dynamical equilibrium selection A. Best-response dynamics B. Stochastic stability C. Learning dynamics D. Comparative Statics: emergence of coordination on general random networks E. Payoff dominance vs. risk dominance VI. Conclusions

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Best reply structure and equilibrium convergence in generic games

Abstract: We offer a new approach to understanding convergence to equilibrium in game theory, inspired by ecology and statistical mechanics.

Cited by 28 publications

References 58 publications

Thermodynamic selection: mechanisms and scenarios

Thermodynamic selection: mechanisms and scenarios

A Fair Governance: On Inequality, Power and Democracy

Coordination problems on networks revisited: statics and dynamics

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