Hardy-Weinberg Equilibrium and Mixed Strategy Equilibrium in Game Theory

AbstractThe Hotelling game of pure location allows interpretations in spatial competition, political theory, and strategic forecasting. In this paper, the doubly symmetric mixed-strategy equilibrium for

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Biological auctions with multiple rewards

Proceedings of The Royal Society B Biological Sciences ◽

10.1098/rspb.2015.1041 ◽

2015 ◽

Vol 282 (1812) ◽

pp. 20151041 ◽

Cited By ~ 4

Author(s):

Johannes G. Reiter ◽

Ayush Kanodia ◽

Raghav Gupta ◽

Martin A. Nowak ◽

Krishnendu Chatterjee

Keyword(s):

Mixed Strategy ◽

Evolutionarily Stable Strategy ◽

Fundamental Characteristic ◽

Stable Strategy ◽

Bidding Strategies ◽

Multiple Resources ◽

Mixed Strategy Equilibrium ◽

Strategy Equilibrium ◽

Evolutionarily Stable ◽

Competition For Resources

The competition for resources among cells, individuals or species is a fundamental characteristic of evolution. Biological all-pay auctions have been used to model situations where multiple individuals compete for a single resource. However, in many situations multiple resources with various values exist and single reward auctions are not applicable. We generalize the model to multiple rewards and study the evolution of strategies. In biological all-pay auctions the bid of an individual corresponds to its strategy and is equivalent to its payment in the auction. The decreasingly ordered rewards are distributed according to the decreasingly ordered bids of the participating individuals. The reproductive success of an individual is proportional to its fitness given by the sum of the rewards won minus its payments. Hence, successful bidding strategies spread in the population. We find that the results for the multiple reward case are very different from the single reward case. While the mixed strategy equilibrium in the single reward case with more than two players consists of mostly low-bidding individuals, we show that the equilibrium can convert to many high-bidding individuals and a few low-bidding individuals in the multiple reward case. Some reward values lead to a specialization among the individuals where one subpopulation competes for the rewards and the other subpopulation largely avoids costly competitions. Whether the mixed strategy equilibrium is an evolutionarily stable strategy (ESS) depends on the specific values of the rewards.

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Bundling and Competition for Slots

The American Economic Review ◽

10.1257/aer.102.5.1957 ◽

2012 ◽

Vol 102 (5) ◽

pp. 1957-1985 ◽

Cited By ~ 8

Author(s):

Doh-Shin Jeon ◽

Domenico Menicucci

Keyword(s):

Marginal Cost ◽

Mixed Strategy ◽

Pure Strategy ◽

Policy Implications ◽

Digital Goods ◽

Efficient Technology ◽

Pure Strategy Equilibrium ◽

Clear Cut ◽

Mixed Strategy Equilibrium ◽

Strategy Equilibrium

We consider competition between sellers selling multiple distinct products to a buyer having k slots. Under independent pricing, a pure strategy equilibrium often does not exist, and equilibrium in mixed strategy is never efficient. When bundling is allowed, each seller has an incentive to bundle his products, and an efficient “technology-renting” equilibrium always exists. Furthermore, in the case of digital goods or when sales below marginal cost are banned, all equilibria are efficient. Comparing the mixed-strategy equilibrium with the technology-renting equilibrium reveals that bundling often increases the buyer's surplus. Finally, we derive clear-cut policy implications.(JEL D43, D86, K21, L13, L14, L41, L82)

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A Ricardian excursion to Bermuda: an estimation of mixed strategy equilibrium

Applied Economics ◽

10.1080/00036849400000054 ◽

1994 ◽

Vol 26 (9) ◽

pp. 927-936 ◽

Cited By ~ 6

Author(s):

Ram Mudambi

Keyword(s):

Mixed Strategy ◽

Mixed Strategy Equilibrium ◽

Strategy Equilibrium

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On the Foundations of Nash Equilibrium

Economics and Philosophy ◽

10.1017/s0266267100003722 ◽

1996 ◽

Vol 12 (1) ◽

pp. 67-88 ◽

Cited By ~ 6

Author(s):

Hans Jørgen Jacobsen

Keyword(s):

Game Theory ◽

Nash Equilibrium ◽

Cooperative Game Theory ◽

Mixed Strategy ◽

Pure Strategy ◽

Mixed Strategies ◽

Positive Theory ◽

Equilibrium Concept ◽

Strategy Equilibrium ◽

Pure Strategies

The most important analytical tool in non-cooperative game theory is the concept of a Nash equilibrium, which is a collection of possibly mixed strategies, one for each player, with the property that each player's strategy is a best reply to the strategies of the other players. If we do not go into normative game theory, which concerns itself with the recommendation of strategies, and focus instead entirely on the positive theory of prediction, two alternative interpretations of the Nash equilibrium concept are predominantly available.In the more traditional one, a Nash equilibrium is a prediction of actual play. A game may not have a Nash equilibrium in pure strategies, and a mixed strategy equilibrium may be difficult to incorporate into this interpretation if it involves the idea of actual randomization over equally good pure strategies. In another interpretation originating from Harsanyi (1973a), see also Rubinstein (1991), and Aumann and Brandenburger (1991), a Nash equilibrium is a ‘consistent’ collection of probabilistic expectations, conjectures, on the players. It is consistent in the sense that for each player each pure strategy, which has positive probability according to the conjecture about that player, is indeed a best reply to the conjectures about others.

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