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Game theory is the study of mathematical models of strategic interactions among rational agents. It has applications in many fields of social science, used extensively in economics as well as in logic, systems science and computer science. Traditional game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 21st century, game theory applies to a wider range of behavioral relations, and it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers.
Zero-sum game is a mathematical representation in game theory and economic theory of a situation that involves two sides, 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 that involves two rational agents, each of whom can cooperate for mutual benefit or betray their partner ("defect") for individual reward. This dilemma was originally framed by Merrill Flood and Melvin Dresher in 1950 while they worked at the RAND Corporation. Albert W. Tucker later formalized the game by structuring the rewards in terms of prison sentences and named it the "prisoner's dilemma".
In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equilibrium strategies of the other players, and no one has anything to gain by changing only one's own strategy. The principle of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to competing firms choosing outputs.
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.
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, 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. It would be much better for each hunter, acting individually, to give up total autonomy and minimal risk, which brings only the small reward of the hare. Instead, each hunter should separately choose the more ambitious and far more rewarding goal of getting the stag, thereby 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.
The public goods game is a standard of experimental economics. In the basic game, subjects secretly choose how many of their private tokens to put into a public pot. The tokens in this pot are multiplied by a factor and this "public good" payoff is evenly divided among players. Each subject also keeps the tokens they do not contribute.
In game theory, folk theorems are a class of theorems describing an abundance of Nash equilibrium payoff profiles in repeated games. The original Folk Theorem concerned the payoffs of all the Nash equilibria of an infinitely repeated game. This result was called the Folk Theorem because it was widely known among game theorists in the 1950s, even though no one had published it. Friedman's (1971) Theorem concerns the payoffs of certain subgame-perfect Nash equilibria (SPE) of an infinitely repeated game, and so strengthens the original Folk Theorem by using a stronger equilibrium concept: subgame-perfect Nash equilibria rather than Nash equilibria.
In game theory, the outcome of a game is the ultimate result of a strategic interaction with one or more people, dependant on the choices made by all participants in a certain exchange. It represents the final payoff resulting from a set of actions that individuals can take within the context of the game. Outcomes are pivotal in determining the payoffs and expected utility for parties involved. Game theorists commonly study how the outcome of a game is determined and what factors affect it.
In game theory, a subgame perfect equilibrium is a refinement of a Nash equilibrium used in dynamic games. A strategy profile is a subgame perfect equilibrium if it represents a Nash equilibrium of every subgame of the original game. Informally, this means that at any point in the game, the players' behavior from that point onward should represent a Nash equilibrium of the continuation game, no matter what happened before. Every finite extensive game with perfect recall has a subgame perfect equilibrium. Perfect recall is a term introduced by Harold W. Kuhn in 1953 and "equivalent to the assertion that each player is allowed by the rules of the game to remember everything he knew at previous moves and all of his choices at those moves".
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.
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 gift-exchange game, also commonly known as the gift exchange dilemma, is a common economic game introduced by George Akerlof and Janet Yellen to model reciprocacy in labor relations. The gift-exchange game simulates a labor-management relationship execution problem in the principal-agent problem in labor economics. The simplest form of the game involves two players – an employee and an employer. The employer first decides whether they should award a higher salary to the employee. The employee then decides whether to reciprocate with a higher level of effort due to the salary increase or not. Like trust games, gift-exchange games are used to study reciprocity for human subject research in social psychology and economics. If the employer pays extra salary and the employee puts in extra effort, then both players are better off than otherwise. The relationship between an investor and an investee has been investigated as the same type of a game.
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.
