Questions tagged [repeated-games]

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Proof of a lemma about PPE

Dear all, I am studying the repeated game with imperfect monitoring. I have so many questions about the proof of lemma 3.6 in slide 22. First of all, why we can write $$ P_{\widehat{\sigma}_{i}, \...
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How does this reporting correspondence is redefined?

Let $\mathcal{R}_i$ be a non-empty, finite set and define the reporting correspondence $R_i:S→2^{\mathcal{R}_i}-\{\emptyset\}$ to be a mapping from player i’s type space to the collection of subsets ...
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How to show that a strategy is a SPNE in repeated games

Consider the down below which I have trouble with solving. For part 1) I have said that a possible outcome path is to play $(D,D)$ in the first round and for all rounds following until $i \leq 298$. ...
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Simultaneous vs Sequential Games [closed]

Is there a way to characterize the distinction between simultaneous vs sequential games? I'm trying to describe a situation where players can only take actions without knowledge of other players' ...
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Finitely repeated Prisoner’s Dilemma with switching cost

I'm doing this finitely repeated Prisoner's dilemma with switching costs but I have trouble showing the fact that $\varepsilon$ had to be $1 < \varepsilon < 2$. I do see why and that it is a ...
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Infinitely repeated game with stationary and symmetric equilibrium

We have two players playing a repeated game. At every period, each player decides to stay or to quit. If both decide to stay, then they both receive 1. If either decides to quit, then the quitter ...
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Finitely repeated prisoner's dilemma without sub-game perfection

Suppose that two individuals play the prisoner's dilemma (PD) a finite number of times; and assume that they both discount the future at a constant rate. Can cooperation be sustained by a Nash ...
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Could someone help guide me on finding the players with perfect recall, and those without?

Could someone help guide me on finding the players with perfect recall, and those without? For those players that do not have perfect recall, what do they forget? Step-by-step guidance would be ...
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Discount factor and deviating from strategy - Game Theory

I have an exercise in Steven Tadelis Game theory Introduction book (10.2) : Grim Trigger: Consider the infinitely repeated game with discount factor $δ < 1$ of the following variant of the Prisoner’...
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3 answers
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Why is the tat-for-tat strategy a Nash equilibrium in infinitely repeated games?

Why is the tat-for-tat strategy a Nash equilibrium in infinitely repeated games, but not a Nash equilibrium in a finite scenario? Specifically for this matrix: Assume higher payoffs reflect higher ...
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2 votes
1 answer
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Simple hawk-dove type super-game

We have the following super-game: \begin{array}{cc} & a_1 & a_2 \\ a_1 & 0,0 & -1,1 \\ a_2 & 1,-1 & -2,-2 \end{array} I want to show that both the trigger (or grim) ...
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Penance strategy game theory

I am having some difficulty in understanding the following use of the penance strategy as a strategy to support compliance in the repeated game presented in Asheim et al. (2006). I understand penance ...
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Clarification of iterated prisoners dilemma

In the description of an iterated prisoner's dilemma on Wikipedia, it states that in order for a game to be considered iterable, it must conform to the rule 2R > T + S, where R is the reward for ...
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Repeated Game SPNE

I approached this question in this way: $(P_1,P_2), (R_1,R_2), (S_1,S_2)$ are the Nash Equilibria of the Stage 1 game. For the given strategy to be sustained as SPNE, there should be no way unilateral ...
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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 ...
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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^{...
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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-...
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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 ...
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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, ...
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1 answer
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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 ...
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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 ...
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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,\...
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2 answers
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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 ...
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3 votes
2 answers
226 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 ...
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5 votes
1 answer
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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 ...
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6 votes
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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{...
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8 votes
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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 ...
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1 vote
1 answer
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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 Nash ...
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2 votes
1 answer
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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 ...
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4 votes
3 answers
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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 ...
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