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Results tagged with game-theory
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user 385
Game theory is a study of situations of strategic interaction between two or more players in which there is a predefined set of rules and an outcome associated with each choice taken.
4
votes
1
answer
674
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Monotone transformation of a game
What happens to the Nash equilibria and minimax values of a strategic game, when we take its payoff table and modify all payoffs by raising them to the 3rd power?
My conjecture is that it depends …
- 3,115
1
vote
1
answer
50
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Repeatedly playing an equilibrium in a repeated game
What is a formal proof to this known fact about repeated games?
The situation in which, in every time step, the players play a Nash equilibrium in the basic game unconditioned on history, is a Nas …
- 3,115
1
vote
Accepted
Repeatedly playing an equilibrium in a repeated game
Suppose all players play unconditioned Nash equilibria, except player $i$ who diverts and plays another strategy. The other strategy of player $i$ may depend on history. We have to show that player $i …
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5
votes
1
answer
196
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A feasible rational payoff that is not an equilibrium payoff in the repeated game
The textbook I am currently reading claims that, in an infinitely-repeated game with discount, there might be a payoff vector which is feasible and individually-rational, but it is not an equilibrium …
- 3,115
2
votes
1
answer
69
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Buy-or-sell deal when there is cash shortage
A company is owned by two partners: partner $A$ holds a fraction $a$ and partner $B$ holds a fraction $b$ (with $a+b=1$). Partner $A$ wants to break the partnership. A common procedure for this is tha …
- 3,115
8
votes
1
answer
1k
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Real-life applications of repeated games theory
What are some scenarios in which the theory of repeated games have been applied?
I am looking, for example, for scenarios in which a government, a firm or a person accepted a decision which relied up …
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2
votes
0
answers
30
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How much information is required to manipulate a mechanism?
It is well-known that the first-price auction is manipulable, in that a player can improve his utility by bidding less than his true value. But successful manipulation requires information: the player …
- 3,115
2
votes
1
answer
57
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Repeated games with decreasing marginal returns
The standard analysis of repeated games assumes that the payoff of a player from a repeated game is a sum (or arithmetic mean, or discounted sum) of the payoffs in the basic games.
But what if the pl …
- 3,115
4
votes
Economics of forgetting
This topic has been studied widely in the theory of repeated games. See for example:
Robert J. Aumann, Sylvain Sorin: Cooperation and bounded recall, Games and Economic Behavior, Vol. 1, No. 1. (Marc …
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3
votes
2
answers
264
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Payoffs in an infinitely-repeated game with discounting
Consider a game with the following payoff matrix:
3,5 0,0 0,0
0,0 5,3 0,0
0,0 0,0 0,0
Suppose the game is played infinitely many times, and both players have discount factor $\delta$.
…
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1
vote
1
answer
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Revenue-maximizing auction with no free disposal
Myerson has a famous theory that can be used to design truthful auctions maximizing the revenue of the seller. The simplest case is when a seller sells a single item to buyers whose values are indepen …
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