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Questions tagged [repeated-games]

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2
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1answer
40 views

Repeated game with stage game has more than 1 NE

Given the game like Prisoner's dilemma (infinitely undiscounted) and each person has 3 actions in every period: confess defect and kill, and the payoff matrix have 2 NE as (D,D),(K,K). Can I still ...
4
votes
1answer
90 views

Why is the symmetric grim trigger not a Nash?

Consider the stage game: Let $\delta\in(0,1)$ be the discount factor. Let $G$ be the symmetric grim trigger strategy profile. The payoffs are then $$E_{A}(G) = E_{B}(G) = \sum_{i=0}^{\infty}3\delta^{...
2
votes
1answer
60 views

Tit-For-Stat Strategy Best Replies

Let $\delta\in(0,1)$ be the discount factor. Consider the stage game in the infinitely repeated prisoner's dilemma game: The goal is to derive conditions on $\delta$ such that the symmetric tit-for-...
0
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0answers
47 views

Some questions about the Truth Game

I have few questions about this game: There are $2^2\times2^2=16$ strategy profiles (HHht, HHhh, HHtt, HHth...). How can I understand which one is a Nash Equilibrium and which one is not? ‎More in ...
3
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1answer
396 views

Game theory with rational and irrational players

Are there game theoretic models where one player is rational and the other is irrational (i.e., plays with behavioral limitations)? The motivation for this question is that behavioral economics has ...
0
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1answer
42 views

Is it possible to transfer information through strategic games?

Let's say that there are 2 players Player A and Player B, engaged in a set of repeated strategic games. Is it then possible to transfer information from one player, say Player A, to the other player, ...
1
vote
1answer
253 views

Collusion, deviation from equilibrium

Two firms can produce either low (L), medium (M) or high (H) quantity. The payoff matrix is given by: What is the outcome of this game if firms play only once? Suppose the game is played for infinite ...
0
votes
1answer
51 views

Maximum level of profit attainable when discount factor is too low

This is a question I encountered during my undergraduate studies in Industrial Economics. So the question goes like this: Consider two identical firms with constant marginal cost $c$ which ...
8
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0answers
150 views

Proofs in the Appendix A of Sannikov (2007)

I have a few questions about the proofs in Appendix A of Sannikov (2007), Games with Imperfectly Observable Actions in Continuous Time. In lemma 4, when he shows the Lipschitz continuity of $H_a(w,\...
-1
votes
2answers
616 views

Nash Equilibrium of modified Keynes' beauty contest

Recently I conducted a small game among students of our institute. The game was based on Keynes' beauty contest game. The participants had to guess a number between 0 to 100 and the participant whose ...
3
votes
2answers
160 views

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 ...
5
votes
1answer
142 views

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 ...
5
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0answers
222 views

Dynamic Bertrand competition when players take turns

Consider the following game: There are two players, $i\in\{1,2\}$ Time is discrete and runs to infinity during periods $t=\{1,2,\ldots\}$ At eat point in time, players have a price $p_i(t)\in\mathbb{...
8
votes
1answer
635 views

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 ...
1
vote
1answer
41 views

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 Nash ...
2
votes
1answer
38 views

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 ...
4
votes
3answers
241 views

Dominated Strategies in an Infinitely vs Finitely Repeated Game

How does the concept of weak dominance work with infinite games? The abundance of concepts seems to muddy things. In particular, suppose two players play the following game an infinite number of ...