scholarly journals Voluntary redistribution mechanism in asymmetric coordination games

2021 ◽  
Author(s):  
Masaki Aoyagi ◽  
Naoko Nishimura ◽  
Yoshitaka Okano
Keyword(s):  
Nash Equilibrium ◽  
Coordination Games ◽  
Coordination Game ◽  
Positive Transfer ◽  
Coordination Failures ◽  
Redistribution Mechanism ◽  
Conflicting Interests ◽  
The Sacrifice ◽  
Asymmetric Coordination

AbstractAn inequality game is an asymmetric 2 × 2 coordination game in which player 1 earns a substantially higher payoff than player 2 except in the inefficient Nash equilibrium (NE). The two players may have either common or conflicting interests over the two NE. This paper studies a redistribution scheme which allows the players to voluntarily transfer their payoffs after the play of an inequality game. We find that the redistribution scheme induces positive transfer from player 1 to player 2 in both common- and conflicting- interest games, and is particularly effective in increasing efficient coordination and reducing coordination failures in conflicting-interest games. We explain these findings by considering reciprocity by player 1 in response to the sacrifice made by player 2 in achieving efficient coordination in conflicting-interest games.

On the convergence of evolution processes with time-varying mutations and local interaction

2001 ◽  
Vol 38 (2) ◽  
pp. 301-323 ◽  
Author(s):  
Hsiao-Chi Chen ◽  
Yunshyoung Chow
Keyword(s):  
Nash Equilibrium ◽  
Dynamic System ◽  
Convergence Rates ◽  
Evolutionary Model ◽  
Coordination Game ◽  
Local Interaction ◽  
Mutation Rates ◽  
Time Varying ◽  
Long Run ◽  
Long Run Equilibrium

This paper analyzes players’ long-run behavior in an evolutionary model with time-varying mutations under both uniform and local interaction rules. It is shown that a risk-dominant Nash equilibrium in a 2 × 2 coordination game would emerge as the long-run equilibrium if and only if mutation rates do not decrease to zero too fast under both interaction methods. The convergence rates of the dynamic system under both interaction rules are also derived. We find that the dynamic system with local matching may not converge faster than that with uniform matching.

scholarly journals Coordination Games on Weighted Directed Graphs

2021 ◽  
Author(s):  
Krzysztof R. Apt ◽  
Sunil Simon ◽  
Dominik Wojtczak
Keyword(s):  
Nash Equilibrium ◽  
Directed Graphs ◽  
Local Area ◽  
Coordination Games ◽  
Strong Equilibrium ◽  
Polymatrix Games ◽  
Token Ring ◽  
Network Topologies ◽  
Ring Protection ◽  
Natural Classes

We study strategic games on weighted directed graphs, where each player’s payoff is defined as the sum of the weights on the edges from players who chose the same strategy, augmented by a fixed nonnegative integer bonus for picking a given strategy. These games capture the idea of coordination in the absence of globally common strategies. We identify natural classes of graphs for which finite improvement or coalition-improvement paths of polynomial length always exist, and consequently a (pure) Nash equilibrium or a strong equilibrium can be found in polynomial time. The considered classes of graphs are typical in network topologies: simple cycles correspond to the token ring local area networks, whereas open chains of simple cycles correspond to multiple independent rings topology from the recommendation G.8032v2 on Ethernet ring protection switching. For simple cycles, these results are optimal in the sense that without the imposed conditions on the weights and bonuses, a Nash equilibrium may not even exist. Finally, we prove that determining the existence of a Nash equilibrium or of a strong equilibrium is NP-complete already for unweighted graphs, with no bonuses assumed. This implies that the same problems for polymatrix games are strongly NP-hard.

scholarly journals Coordination and Equilibrium Selection in Games: The Role of Local Effects

2021 ◽  
Author(s):  
Tomasz Raducha ◽  
Maxi San Miguel
Keyword(s):  
Replicator Dynamics ◽  
Equilibrium Selection ◽  
System Size ◽  
Critical Value ◽  
Dominant Strategy ◽  
Coordination Games ◽  
Coordination Game ◽  
Local Effects ◽  
Update Rules

Abstract We study the role of local effects and finite size effects in reaching coordination and in equilibrium selection in two-player coordination games. We investigate three update rules – the replicator dynamics (RD), the best response (BR), and the unconditional imitation (UI). For the pure coordination game with two equivalent strategies we find a transition from a disordered state to coordination for a critical value of connectivity. The transition is system-size-independent for the BR and RD update rules. For the IU it is system-size-dependent, but coordination can always be reached below the connectivity of a complete graph. We also consider the general coordination game which covers a range of games, such as the stag hunt. For these games there is a payoff-dominant strategy and a risk-dominant strategy with associated states of equilibrium coordination. We analyse equilibrium selection analytically and numerically. For the RD and BR update rules mean-field predictions agree with simulations and the risk-dominant strategy is evolutionary favoured independently of local effects. When players use the unconditional imitation, however, we observe coordination in the payoff-dominant strategy. Surprisingly, the selection of pay-off dominant equilibrium only occurs below a critical value of the network connectivity and disappears in complete graphs. As we show, it is a combination of local effects and update rule that allows for coordination on the payoff-dominant strategy.

scholarly journals Coordination on networks with farsighted and myopic agents

2022 ◽  
Author(s):  
Ana Mauleon ◽  
Simon Schopohl ◽  
Akylai Taalaibekova ◽  
Vincent Vannetelbosch
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Policy Instruments ◽  
Coordination Game ◽  
Equilibrium Strategy ◽  
Social Planner ◽  
Stable Strategy ◽  
Nash Equilibrium Strategy ◽  
Connected Network ◽  
Ex Ante

AbstractWe study a coordination game on a fixed connected network where players have to choose between two projects. Some players are moderate (i.e. they are ex-ante indifferent between both projects) while others are stubborn (i.e. they always choose the same project). Benefits for moderate players are increasing in the number of neighbors who choose the same project. In addition, players are either farsighted or myopic. Farsighted players anticipate the reactions of others while myopic players do not. We show that, when all players are farsighted, full coordination among the moderate players is reached except if there are stubborn players for both projects. When the population is mixed, the set of stable strategy profiles is a refinement of the set of Nash equilibrium strategy profiles. In fact, turning myopic players into farsighted ones eliminates gradually the inefficient Nash equilibria. Finally, we consider a social planner who can improve coordination by means of two policy instruments: adding links to the network (socialization) and/or turning myopic players into farsighted ones (education).

ANTI-COORDINATION GAMES AND DYNAMIC STABILITY

2007 ◽  
Vol 09 (04) ◽  
pp. 667-688 ◽  
Author(s):  
FUHITO KOJIMA ◽  
SATORU TAKAHASHI
Keyword(s):  
Dynamic Stability ◽  
Mixed Strategy ◽  
Large Population ◽  
Initial Distribution ◽  
Coordination Games ◽  
Coordination Game ◽  
Initial State ◽  
Coordination Property ◽  
Best Response ◽  
Best Response Dynamic

We introduce the class of anti-coordination games. A symmetric two-player game is said to have the anti-coordination property if, for any mixed strategy, any worst response to the mixed strategy is in the support of the mixed strategy. Every anti-coordination game has a unique symmetric Nash equilibrium, which lies in the interior of the set of mixed strategies. We investigate the dynamic stability of the equilibrium in a one-population setting. Specifically we focus on the best response dynamic (BRD), where agents in a large population take myopic best responses, and the perfect foresight dynamic (PFD), where agents maximize total discounted payoffs from the present to the future. For any anti-coordination game we show (i) that, for any initial distribution, BRD has a unique solution, which reaches the equilibrium in a finite time, (ii) that the same path is one of the solutions to PFD, and (iii) that no path escapes from the equilibrium in PFD once the path reaches the equilibrium. Moreover we show (iv) that, in some subclasses of anti-coordination games, for any initial state, any solution to PFD converges to the equilibrium. All the results for PFD hold for any discount rate.

scholarly journals Language, Meaning, and Games: A Model of Communication, Coordination, and Evolution

2008 ◽  
Vol 98 (4) ◽  
pp. 1292-1311 ◽  
Author(s):  
Stefano Demichelis ◽  
Jörgen W Weibull
Keyword(s):  
Nash Equilibrium ◽  
Cheap Talk ◽  
Coordination Games ◽  
Natural Languages ◽  
Efficient Outcome ◽  
Pareto Efficient ◽  
Evolutionarily Stable ◽  
Language Meaning

Language is a powerful coordination device. We generalize the cheap-talk approach to pre-play communication by way of introducing a meaning correspondence between messages and actions, and by postulating two axioms met by natural languages. Players have a lexicographic preference, second to material payoffs, against deviating from the meaning correspondence. Under two-sided communication in generic and symmetric n × n-coordination games, a Nash equilibrium component in such a lexicographic communication game is evolutionarily stable if and only if it results in the unique Pareto efficient outcome of the underlying game. We extend the analysis to one-sided communication in arbitrary finite two-player games. (JEL C72, C73, Z13)

scholarly journals Coordination games in cancer

2021 ◽  
Author(s):  
Peter Bayer ◽  
Robert Gatenby ◽  
Patricia H. McDonald ◽  
Derek R. Duckett ◽  
Katerina Stankova ◽  
...  
Keyword(s):  
Tumor Growth ◽  
Public Goods ◽  
Cancer Cells ◽  
Evolutionary Games ◽  
Coordination Games ◽  
Coordination Game ◽  
Public Goods Games ◽  
Cancer Initiation ◽  
Dependent Cell ◽  
Model Frequency

We propose a model of cancer initiation and progression where tumor growth is modulated by an evolutionary coordination game. Evolutionary games of cancer are widely used to model frequency-dependent cell interactions with the most studied games being the Prisoner's Dilemma and public goods games. Coordination games, by their more obscure and less evocative nature, are left understudied, despite the fact that, as we argue, they offer great potential in understanding and treating cancer. In this paper we present the conditions under which coordination games between cancer cells evolve, we propose aspects of cancer that can be modeled as results of coordination games, and explore the ways through which coordination games of cancer can be exploited for therapy.

scholarly journals Evolutionary Network Games: Equilibria from Imitation and Best Response Dynamics

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Giulio Cimini
Keyword(s):  
Large Scale ◽  
Nash Equilibria ◽  
Evolutionary Dynamics ◽  
Mean Field ◽  
Coordination Games ◽  
Coordination Game ◽  
Strategic Substitutes ◽  
Response Dynamics ◽  
Scale Free ◽  
Best Response

We consider games of strategic substitutes and complements on networks and introduce two evolutionary dynamics in order to refine their multiplicity of equilibria. Within mean field, we find that for the best-shot game, taken as a representative example of strategic substitutes, replicator-like dynamics does not lead to Nash equilibria, whereas it leads to a unique equilibrium for complements, represented by a coordination game. On the other hand, when the dynamics becomes more cognitively demanding, predictions are always Nash equilibria: for the best-shot game we find a reduced set of equilibria with a definite value of the fraction of contributors, whereas, for the coordination game, symmetric equilibria arise only for low or high initial fractions of cooperators. We further extend our study by considering complex topologies through heterogeneous mean field and show that the nature of the selected equilibria does not change for the best-shot game. However, for coordination games, we reveal an important difference: on infinitely large scale-free networks, cooperative equilibria arise for any value of the incentive to cooperate. Our analytical results are confirmed by numerical simulations and open the question of whether there can be dynamics that consistently leads to stringent equilibria refinements for both classes of games.

The Tower of Babel as a Coordination Game: Political Linguistics in Ghana

1994 ◽  
Vol 88 (3) ◽  
pp. 622-634 ◽  
Author(s):  
David D. Laitin
Keyword(s):  
Empirical Data ◽  
Coordination Games ◽  
Coordination Game ◽  
Indigenous Language ◽  
Official Language ◽  
Equilibrium Outcome ◽  
Tower Of Babel ◽  
Language Outcome ◽  
Political Linguistics ◽  
Theoretic Solution

The problem of choosing an indigenous official language for multilingual states in general and for Ghana in particular is treated as one of coordination in an n-person tipping game. Even with an assumption that the equilibrium outcome of all-English is deficient, the mechanisms for reaching an indigenous language solution are difficult to find. A lottery (a theoretically attractive approach to the solution of coordination games) is less attractive when applied to the issue of language coordination. Empirical data based on interviews from six different regions of Ghana show the limits and possibilities of the theoretic solution. Going back to theory, a mechanism for the successful promotion of an indigenous language outcome is proposed.

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