7 votes
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Real-life applications of repeated games theory

I believe insights from repeated game theory have been used in designing the assignment scheme for security patrols in many occasions. In this matter, the main research projects with close ...
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6 votes
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Finitely repeated Prisoner’s Dilemma with switching cost

A couple hints. Regarding the lower bound on $\epsilon$: What happens if deviation occurs at stage $T$? In other words, there is no opportunity for your so-called "punishment stages". ...
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5 votes
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A feasible rational payoff that is not an equilibrium payoff in the repeated game

It is true because of the discounting. If the discount parameter were $\delta = 1$ then players 1 and 2 could alternate playing TL and MR in equilibrium and then reach the average payoff vector $1,1,5$...
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5 votes
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Finitely repeated prisoner's dilemma without sub-game perfection

There is also no NE which sustains coopration for more or less the same reason as in the SPNE case. Consider, a PD played twice. A strategy contains five actions, one for each decision node: one in ...
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  • 5,090
4 votes
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Game theory with rational and irrational players

Yes, a whole book has been written on Behavioral Game Theory. More specifically, standard solution concept such as Nash equilibrium requires that players best respond to a correct belief about other ...
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3 votes

Infinitely repeated game with stationary and symmetric equilibrium

Why don't you attack the problem straighrforwardly and investigate the profitability of a deviation? Suppose there was a Nash equilibrium in which both players decide to stay forever. Both players ...
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3 votes
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Clarification of iterated prisoners dilemma

The payoff depends entirely on how you set the game up. Here's one example of the case where $2R \leq T + S$: ...
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3 votes

Why is the tat-for-tat strategy a Nash equilibrium in infinitely repeated games?

(i) In the 1 round case, tit-for-tat is not a NE. To see this notice that the tit-for-tat strategy, as you describe, dictates that the players play $(H,H)$ in the first (and only) round---as you point ...
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  • 946
3 votes

Dominated Strategies in an Infinitely vs Finitely Repeated Game

The problem you mentioned is why dominance is not really used frequently. It is a very weak concept in the sense that is usually has no "grip", i.e. not many strategies are eliminated. That is why we ...
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3 votes

Dominated Strategies in an Infinitely vs Finitely Repeated Game

A usual refinement concept used to deal with weakly dominated strategies is the trembling hand perfect equilibrium. (I do not know others but this one works quite well. The strategy in question is ...
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2 votes

Payoffs in an infinitely-repeated game with discounting

I am going to construct pure strategies, taking average payoffs so far as a state variable, that achieve the payoffs $(4,4)$ in the infinitely repeated game. Call the row player's actions $T$, $M$, ...
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2 votes

Payoffs in an infinitely-repeated game with discounting

Disclaimer: I only have a slight clue about repeated games and I have virtually no clue about coding (except the compulsory stuff I had to do in grad school). That being said, consider this stream of ...
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  • 5,090
2 votes
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Nash Equilibrium of modified Keynes' beauty contest

Assume the players have to choose integers, otherwise a best response may not exist. Let the payoff of winning be $\alpha\cdot[\frac23\text{ of the average}]$, $\alpha>0$. Consider the two player (...
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2 votes
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Penance strategy game theory

I see two ways to produce histories with multi-state deviations (not including the degenerate case in which all states defect): Multiple states defect in different periods. This possibility is ruled ...
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  • 1,798
2 votes
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Simultaneous vs Sequential Games

In the standard theory of games, simultaneous and sequential games are distinguished by the means of something called "Information Sets". Alluding to the origins of Game Theory (von Neumann ...
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  • 308
1 vote
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How does this reporting correspondence is redefined?

Without this being a clear answer onge thought could be to define the reporting correspondence as it follows $$R_i^t(s_i^t|h^{t-1})=\{s_i^t\in S_i^t\quad \text{where player $i$ reports truthfully her ...
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1 vote

How to show that a strategy is a SPNE in repeated games

For the first part: correct, any NE in the stage game is a SPNE in an repeated game. In fact, it is the only SPNE if the game is repeated finitely many times. For the second part: to check that a ...
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1 vote

Could someone help guide me on finding the players with perfect recall, and those without?

Hint: A player with perfect recall means the player remembers the history of the moves up to the current information set. In particular, he remembers the previous actions he has taken. Now in Player $\...
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1 vote
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Repeated Game SPNE

In a finitely repeated game with a unique NE, the only SPNE is the repetition of the unique NE. The reason is that by backward induction the NE will be played in the last period and, hence, also in ...
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  • 5,090
1 vote

Repeated game with stage game has more than 1 NE

Though a bit unconventional to assume an infinitely repeated game without discounting, the short answer to your question is: yes. Any sequence of stage game Nash Equilibria is supportable as a SPNE. ...
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  • 1,370
1 vote

Is it possible to transfer information through strategic games?

What you are implying is thoroughly studied by what is called algorithmic game theory. There you can find the concept of a learning algorithm. In game theoretical scenarios where the mathematical ...
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1 vote
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Collusion, deviation from equilibrium

Converting my comments into an answer... In the infinitely repeated game, if the players want to collude on $(L,L)$, then there needs to be an incentive for each to stick to the plan, i.e. a ...
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1 vote
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Maximum level of profit attainable when discount factor is too low

I do not want to do all the algebra, but I give you a hint. You are correct: You are asked about $\pi^C$ in your Condition (1) and you are also right that $\pi^D$ changes. In your parameter setting ...
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  • 5,090
1 vote

Nash Equilibrium of modified Keynes' beauty contest

@denesp nailed the answer on the head. This is not different from the original game in any meaningful way, therefore, the nash equilibrium remains the same. Size of payouts don't change the outcome ...
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  • 661
1 vote
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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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1 vote
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Repeated games with decreasing marginal returns

It seems to me that this will not make a difference if you only consider pure strategies. Consider that player $i$'s winnings is $x$ and from this he gets utility $U_i(x)$. As long as $U_i()$ is ...
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