7
votes
Accepted
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 ...
- 5,167
6
votes
Accepted
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".
...
- 14.4k
5
votes
Accepted
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 $1,1,5$...
- 26.2k
5
votes
Accepted
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 ...
- 5,090
4
votes
Accepted
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 ...
- 14.4k
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 ...
- 5,090
3
votes
Accepted
Clarification of iterated prisoners dilemma
The payoff depends entirely on how you set the game up. Here's one example of the case where $2R \leq T + S$:
...
- 2,764
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 ...
- 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 ...
- 1,682
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 ...
- 26.2k
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 $T$, $M$, ...
- 2,097
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 ...
- 5,090
2
votes
Accepted
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 (...
- 14.4k
2
votes
Accepted
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 ...
- 1,798
2
votes
Accepted
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 ...
- 308
1
vote
Accepted
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 ...
- 929
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 ...
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 $\...
- 14.4k
1
vote
Accepted
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 ...
- 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. ...
- 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 ...
- 299
1
vote
Accepted
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 ...
- 14.4k
1
vote
Accepted
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 ...
- 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 ...
- 661
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 $i$...
- 2,905
1
vote
Accepted
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 ...
- 26.2k
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