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An evolutionarily stable strategy (ESS) is a strategy that is impermeable when adopted by a population in adaptation to a specific environment, that is to say it cannot be displaced by an alternative strategy which may be novel or initially rare. Introduced by John Maynard Smith and George R. Price in 1972/3, it is an important concept in behavioural ecology, evolutionary psychology, mathematical game theory and economics, with applications in other fields such as anthropology, philosophy and political science.
Zero-sum game is a mathematical representation in game theory and economic theory of a situation that involves two competing entities, where the result is an advantage for one side and an equivalent loss for the other. In other words, player one's gain is equivalent to player two's loss, with the result that the net improvement in benefit of the game is zero.
The prisoner's dilemma is a game theory thought experiment involving two rational agents, each of whom can either cooperate for mutual benefit or betray their partner ("defect") for individual gain. The dilemma arises from the fact that while defecting is rational for each agent, cooperation yields a higher payoff for each. The puzzle was designed by Merrill Flood and Melvin Dresher in 1950 during their work at the RAND Corporation. They invited economist Armen Alchian and mathematician John Williams to play a hundred rounds of the game, observing that Alchian and Williams often chose to cooperate. When asked about the results, John Nash remarked that rational behavior in the iterated version of the game can differ from that in a single-round version. This insight anticipated a key result in game theory: cooperation can emerge in repeated interactions, even in situations where it is not rational in a one-off interaction.
In game theory, the Nash equilibrium is the most commonly-used solution concept for non-cooperative games. A Nash equilibrium is a situation where no player could gain by changing their own strategy. The idea of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to his model of competition in an oligopoly.
In the social sciences, bargaining or haggling is a type of negotiation in which the buyer and seller of a good or service debate the price or nature of a transaction. If the bargaining produces agreement on terms, the transaction takes place. It is often commonplace in poorer countries, or poorer localities within any specific country. Haggling can mostly be seen within street markets worldwide, wherein there remains no guarantee of the origin and authenticity of available products. Many people attribute it as a skill, but there remains no guarantee that the price put forth by the buyer would be acknowledged by the seller, resulting in losses of profit and even turnover in some cases. A growth in the country's GDP Per Capita Income is bound to reduce both the ill-effects of bargaining and the unscrupulous practices undertaken by vendors at street markets.
The game of chicken, also known as the hawk-dove game or snowdrift game, is a model of conflict for two players in game theory. The principle of the game is that while the ideal outcome is for one player to yield, individuals try to avoid it out of pride, not wanting to look like "chickens." Each player taunts the other to increase the risk of shame in yielding. However, when one player yields, the conflict is avoided, and the game essentially ends.
Evolutionary game theory (EGT) is the application of game theory to evolving populations in biology. It defines a framework of contests, strategies, and analytics into which Darwinian competition can be modelled. It originated in 1973 with John Maynard Smith and George R. Price's formalisation of contests, analysed as strategies, and the mathematical criteria that can be used to predict the results of competing strategies.
A coordination game is a type of simultaneous game found in game theory. It describes the situation where a player will earn a higher payoff when they select the same course of action as another player. The game is not one of pure conflict, which results in multiple pure strategy Nash equilibria in which players choose matching strategies. Figure 1 shows a 2-player example.
In game theory, a non-cooperative game is a game in which there are no external rules or binding agreements that enforce the cooperation of the players. A non-cooperative game is typically used to model a competitive environment. This is stated in various accounts most prominent being John Nash's 1951 paper in the journal Annals of Mathematics.
In game theory, grim trigger is a trigger strategy for a repeated game.
In game theory, the stag hunt, sometimes referred to as the assurance game, trust dilemma or common interest game, describes a conflict between safety and social cooperation. The stag hunt problem originated with philosopher Jean-Jacques Rousseau in his Discourse on Inequality. In the most common account of this dilemma, which is quite different from Rousseau's, two hunters must decide separately, and without the other knowing, whether to hunt a stag or a hare. However, both hunters know the only way to successfully hunt a stag is with the other's help. One hunter can catch a hare alone with less effort and less time, but it is worth far less than a stag and has much less meat. But both hunters would be better off if both choose the more ambitious and more rewarding goal of getting the stag, giving up some autonomy in exchange for the other hunter's cooperation and added might. This situation is often seen as a useful analogy for many kinds of social cooperation, such as international agreements on climate change.
Quantum game theory is an extension of classical game theory to the quantum domain. It differs from classical game theory in three primary ways:
- Superposed initial states,
- Quantum entanglement of initial states,
- Superposition of strategies to be used on the initial states.
In game theory, the traveler's dilemma is a non-zero-sum game in which each player proposes a payoff. The lower of the two proposals wins; the lowball player receives the lowball payoff plus a small bonus, and the highball player receives the same lowball payoff, minus a small penalty. Surprisingly, the Nash equilibrium is for both players to aggressively lowball. The traveler's dilemma is notable in that naive play appears to outperform the Nash equilibrium; this apparent paradox also appears in the centipede game and the finitely-iterated prisoner's dilemma.
Bargaining power is the relative ability of parties in an argumentative situation to exert influence over each other in order to achieve favourable terms in an agreement. This power is derived from various factors such as each party’s alternatives to the current deal, the value of what is being negotiated, and the urgency of reaching an agreement. A party's bargaining power can significantly shift the outcome of negotiations, leading to more advantageous positions for those who possess greater leverage.
Cooperative bargaining is a process in which two people decide how to share a surplus that they can jointly generate. In many cases, the surplus created by the two players can be shared in many ways, forcing the players to negotiate which division of payoffs to choose. Such surplus-sharing problems are faced by management and labor in the division of a firm's profit, by trade partners in the specification of the terms of trade, and more.
A Markov perfect equilibrium is an equilibrium concept in game theory. It has been used in analyses of industrial organization, macroeconomics, and political economy. It is a refinement of the concept of subgame perfect equilibrium to extensive form games for which a pay-off relevant state space can be identified. The term appeared in publications starting about 1988 in the work of economists Jean Tirole and Eric Maskin.
Program equilibrium is a game-theoretic solution concept for a scenario in which players submit computer programs to play the game on their behalf and the programs can read each other's source code. The term was introduced by Moshe Tennenholtz in 2004. The same setting had previously been studied by R. Preston McAfee, J. V. Howard and Ariel Rubinstein.
Sequential bargaining is a structured form of bargaining between two participants, in which the participants take turns in making offers. Initially, person #1 has the right to make an offer to person #2. If person #2 accepts the offer, then an agreement is reached and the process ends. If person #2 rejects the offer, then the participants switch turns, and now it is the turn of person #2 to make an offer. The people keep switching turns until either an agreement is reached, or the process ends with a disagreement due to a certain end condition. Several end conditions are common, for example:
The Berge equilibrium is a game theory solution concept named after the mathematician Claude Berge. It is similar to the standard Nash equilibrium, except that it aims to capture a type of altruism rather than purely non-cooperative play. Whereas a Nash equilibrium is a situation in which each player of a strategic game ensures that they personally will receive the highest payoff given other players' strategies, in a Berge equilibrium every player ensures that all other players will receive the highest payoff possible. Although Berge introduced the intuition for this equilibrium notion in 1957, it was only formally defined by Vladislav Iosifovich Zhukovskii in 1985, and it was not in widespread use until half a century after Berge originally developed it.
References
- ↑ Ilwoo Hwang (May 2018). "A theory of bargaining deadlock" (PDF). Games and Economic Behavior. 109: 501–522. doi:10.1016/j.geb.2018.02.002.
