The one-shot deviation principle (also known as one-deviation property) is the principle of optimality of dynamic programming applied to game theory. It says that a strategy profile of a finite extensive-form game is a subgame perfect equilibrium (SPE) if and only if there exist no profitable one-shot deviations for each subgame and every player.
What is a one shot game?
One-Shot Games. This is a game that is played only once. The pay-off may be such that a game might be impossible to play twice. E.g. mutually assured nuclear destruction. Slightly different with tactical / conventional warfare. In one-shot interaction, people often have an incentive to behave opportunistically / selfishly.
Is a one-shot strategy better than a repeated game?
In a one-shot game, such as our previous example of the prisoner's dilemma, the stakes are high -- but carry no further repercussions. However, when playing a repeated game, a one-shot strategy may not be the best move: You and your opponent can get better returns in the long run by cooperating (not confessing)...
What is the one-shot deviation principle?
One-shot deviation principle. The one-shot deviation principle (also known as one-deviation property) is the principle of optimality of dynamic programming applied to game theory. It says that a strategy profile of a finite extensive-form game is a subgame perfect equilibrium (SPE) if and only if there exist no profitable one-shot...
What is a collusive strategy in a one shot game?
In a one-shot game, a collusive strategy always represents a Nash equilibrium B. A perfect equilibrium occurs when each player is doing the best he can regardless of what the other player is doing
What is a one-shot game game theory?
– One-shot game: game is played once. – Repeated game: game is played more than once; either a finite or infinite number of interactions.
What is one-shot Nash equilibrium?
In a one-shot game, in which each player chooses a strategy from his strategy space and knows that it is a once-and-for-all choice, the Nash equilibrium is a rational way to play the game and when it is unique, it is the only rational way to play the game.
What is a one-shot static game?
• Repetitions: Static games can be played just once, in which case they are called one-shot games, or they may be played repeatedly, in which case they are called repeated games. Real life games of market competition may be modeled as repeated games or as dynamic games. •
Is Prisoner's dilemma a one-shot game?
One of the most widely-used paradigms is the anonymous one-shot prisoner's dilemma game (Luce and Raiffa, 1957). In this game, two interacting players simultaneously choose between cooperating or defecting.
Does every game have a Nash equilibrium?
While Nash proved that every finite game has a Nash equilibrium, not all have pure strategy Nash equilibria. For an example of a game that does not have a Nash equilibrium in pure strategies, see Matching pennies.
Is there Nash equilibrium in prisoner's dilemma?
The likely outcome for a prisoner's dilemma is that both players defect (i.e., behave selfishly), leading to suboptimal outcomes for both. This is also the Nash Equilibrium, a decision-making theorem within game theory that states a player can achieve the desired outcome by not deviating from their initial strategy.
What are the four types of games in game theory?
Different types of game theory include cooperative/non-cooperative, zero-sum/non-zero-sum, and simultaneous/sequential.
What is meant by zero sum game?
A zero-sum game is a situation where, if one party loses, the other party wins, and the net change in wealth is zero. Zero-sum games can include just two players or millions of participants.
What are the types of strategies in game theory?
Therefore on the basis of outcome, the strategies of the game theory are classified as pure and mixed strategies, dominant and dominated strategies, minimax strategy, and maximin strategy.
What is the best strategy for Prisoner's dilemma?
The strategy is simply to cooperate on the first iteration of the game; after that, the player does what his or her opponent did on the previous move. Depending on the situation, a slightly better strategy can be "tit for tat with forgiveness".
What is the key feature of prisoner's dilemma game?
Key Takeaways A prisoner's dilemma describes a situation where, according to game theory, two players acting selfishly will ultimately result in a suboptimal choice for both. The prisoner's dilemma also shows us that mere cooperation is not always in one's best interests.
What do you mean by prisoner's dilemma?
A prisoner's dilemma is a decision-making and game theory paradox illustrating that two rational individuals making decisions in their own self-interest cannot result in an optimal solution. The paradox was developed by mathematicians M. Flood and M.
Why do senators use game theory?
Senators often use game theory principles to garner support for their proposed bills. In a one-shot game, such as our previous example of the prisoner's dilemma, the stakes are high -- but carry no further repercussions. However, when playing a repeated game, a one-shot strategy may not be the best move: You and your opponent can get better returns ...
What is the tit for tat strategy?
Playing a series of games with no known end, the players can adopt a tit-for-tat strategy, which punishes the opponent for defecting.
Why is one shot deviation called one shot deviation?
This is called the one-shot deviation principle because it allows us to check single deviations to find equilibria. It is straightforward to understand that if something is a subgame perfect equilibrium, no profitable one shot deviation exists. SPE must be optimal.
What is a perfect equilibrium in a finite game?
In finite games or infinitely repeated games with discounting, a set of strategies is a subgame perfect equilibrium if and only if no player can profitably deviate from his strategy at a single stage and maintain his strategy everywhere else.
What is one shot deviation?
The one-shot deviation principle (also known as one-deviation property) is the principle of optimality of dynamic programming applied to game theory. It says that a strategy profile of a finite extensive-form game is a subgame perfect equilibrium (SPE) if and only if there exist no profitable one-shot deviations for each subgame and every player. In simpler terms, if no player can increase their payoffs by deviating a single decision, or period, from their original strategy, then the strategy that they have chosen is a SPE. As a result, no player can profit from deviating from the strategy for one period and then reverting to the strategy.
Why is one shot deviation important?
Furthermore, the one-shot deviation principle is very important for infinite horizon games, in which the principle typically does not hold, since it is not plausible to consider an infinite number of strategies and payoffs in order to solve.
What is one shot game?
One-shot games: The play of the game occurs only once. Here, the players are likely to not know much about each other. For example, tipping a waiter on your vacation.
What is game theory?
By. Ashley Crossman. Updated March 01, 2019. Game theory is a theory of social interaction, which attempts to explain the interaction people have with one another. As the name of the theory suggests, game theory sees human interaction as just that: a game. John Nash, the mathematician who was featured in the movie A Beautiful Mind is one ...
How Was Game Theory Developed?
Game theory was originally an economic and mathematical theory that predicted that human interaction had the characteristics of a game, including strategies, winners and losers, rewards and punishment, and profits and cost. It was initially developed to understand a large variety of economic behaviors, including behavior of firms, markets, and consumers. The use of the game theory has since expanded in the social sciences and has been applied to political, sociological, and psychological behaviors as well.
Why is game theory criticized?
This particular view of game theory has been criticized because the assumptions made by the game theorists are often violated. For example, they assume that players always act in a way to directly maximize their wins, when in reality this is not always true. Altruistic and philanthropic behavior would not fit this model.
Why is game theory so controversial?
Game theory was first used to describe and model how human populations behave. Some scholars believe that they can actually predict how actual human populations will behave when confronted with situations analogous to the game being studied. This particular view of game theory has been criticized because the assumptions made by ...
What is a simultaneous move game?
Simultaneous move games: Players choose actions simultaneously. For example, in the Prisoner’s Dilemma (see below), each player must anticipate what their opponent is doing at that moment, recognizing that the opponent is doing the same.
What is zero sum game?
Zero-sum game: The players’ interests are in direct conflict with one another. For example, in football, one team wins and the other team loses. If a win equals +1 and a loss equals -1, the sum is zero.
Background
A one-shot game is one where two participants have some set of actions { 1,..., n }, they make their decision on which option to take (without knowing the decision of their partner, or in sequence depending on game). Based on the action i of the first player and j of the second player, they receive some reward (or punishment) G ( i, j).
Question
Game theory makes predictions on how rational players will behave in such settings. The fun part of psychology is that humans often don't follow these predictions.
Notes
I prefer artificial well-controlled experiments with a large number of participants over natural or in-the-field experiments.