Peace war game is an iterated game originally played in academic groups and by computer simulation for years to study possible strategies of cooperation and aggression.[1] As peace makers became richer over time it became clear that making war had greater costs than initially anticipated. The only strategy that acquired wealth more rapidly was a "Genghis Khan", a constant aggressor making war continually to gain resources. This led to the development of the "provokable nice guy" strategy, a peace-maker until attacked.[2] Multiple players continue to gain wealth cooperating with each other while bleeding the constant aggressor.[2]
The peace war game is a variation of the iterated prisoner's dilemma in which the decisions (Cooperate, Defect) are replaced by (Peace, War). Strategies remain the same with reciprocal altruism, "Tit for Tat", or "provokable nice guy" as the best deterministic one. This strategy is simply to make peace on the first iteration of the game; after that, the player does what his opponent did on the previous move. A slightly better strategy is "Tit for Tat with forgiveness". When the opponent makes war, on the next move, the player sometimes makes peace anyway, with a small probability. This allows an escape from wasting cycles of retribution, a motivation similar to the Rule of Ko in the game of Go. "Tit for Tat with forgiveness" is best when miscommunication is introduced, when one's move is incorrectly reported to the opponent. A typical payoff matrix for two players (A, B) of one iteration of this game is:
Here a player's resources have a value of 2, half of which must be spent to wage war. In this case, there exists a Nash equilibrium, a mutually best response for a single iteration, here (War, War), by definition heedless of consequences in later iterations. "Provokable nice guy's" optimality depends on iterations. How many are necessary is likely tied to the payoff matrix and probabilities of choosing.[3] A subgame perfect version of this strategy is "Contrite Tit-for-Tat" which is to make peace unless one is in "good standing" and one's opponent is not. Good ("standing" assumed) means to make peace with good opponents, make peace when bad, or make war when good and opponent is not.[4]
He who is skilled in war subdues the enemy without fighting.
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.
The Evolution of Cooperation is a 1984 book written by political scientist Robert Axelrod that expands upon a paper of the same name written by Axelrod and evolutionary biologist W.D. Hamilton. The article's summary addresses the issue in terms of "cooperation in organisms, whether bacteria or primates".
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 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 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.
Tit for tat is an English saying meaning "equivalent retaliation". It is an alteration of tip for tap "blow for blow", first recorded in 1558.
In economics and game theory, a participant is considered to have superrationality if they have perfect rationality but assume that all other players are superrational too and that a superrational individual will always come up with the same strategy as any other superrational thinker when facing the same problem. Applying this definition, a superrational player playing against a superrational opponent in a prisoner's dilemma will cooperate while a rationally self-interested player would defect.
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.
In game theory, the best response is the strategy which produces the most favorable outcome for a player, taking other players' strategies as given. The concept of a best response is central to John Nash's best-known contribution, the Nash equilibrium, the point at which each player in a game has selected the best response to the other players' strategies.
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.
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.
Regime theory is a theory within international relations derived from the liberal tradition that argues that international institutions or regimes affect the behavior of states or other international actors. It assumes that cooperation is possible in the anarchic system of states, as regimes are, by definition, instances of international cooperation.
In game theory, a dominant strategy is a strategy that is better than any other strategy for one player, no matter how that player's opponent will play. Some very simple games can be solved using dominance.
A collective action problem or social dilemma is a situation in which all individuals would be better off cooperating but fail to do so because of conflicting interests between individuals that discourage joint action. The collective action problem has been addressed in political philosophy for centuries, but was most clearly established in 1965 in Mancur Olson's The Logic of Collective Action.
Risk dominance and payoff dominance are two related refinements of the Nash equilibrium (NE) solution concept in game theory, defined by John Harsanyi and Reinhard Selten. A Nash equilibrium is considered payoff dominant if it is Pareto superior to all other Nash equilibria in the game.1 When faced with a choice among equilibria, all players would agree on the payoff dominant equilibrium since it offers to each player at least as much payoff as the other Nash equilibria. Conversely, a Nash equilibrium is considered risk dominant if it has the largest basin of attraction. This implies that the more uncertainty players have about the actions of the other player(s), the more likely they will choose the strategy corresponding to it.
Nice Guys Finish First is a 1986 documentary by Richard Dawkins which discusses selfishness and cooperation, arguing that evolution often favors co-operative behaviour, and focusing especially on the tit for tat strategy of the prisoner's dilemma game. The film is approximately 50 minutes long and was produced by Jeremy Taylor.
Subjective expected relative similarity (SERS) is a normative and descriptive theory that predicts and explains cooperation levels in a family of games termed Similarity Sensitive Games (SSG), among them the well-known Prisoner's Dilemma game (PD). SERS was originally developed in order to (i) provide a new rational solution to the PD game and (ii) to predict human behavior in single-step PD games. It was further developed to account for: (i) repeated PD games, (ii) evolutionary perspectives and, as mentioned above, (iii) the SSG subgroup of 2×2 games. SERS predicts that individuals cooperate whenever their subjectively perceived similarity with their opponent exceeds a situational index derived from the game's payoffs, termed the similarity threshold of the game. SERS proposes a solution to the rational paradox associated with the single step PD and provides accurate behavioral predictions. The theory was developed by Prof. Ilan Fischer at the University of Haifa.
Reciprocal altruism in humans refers to an individual behavior that gives benefit conditionally upon receiving a returned benefit, which draws on the economic concept – ″gains in trade″. Human reciprocal altruism would include the following behaviors : helping patients, the wounded, and the others when they are in crisis; sharing food, implement, knowledge.
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