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".
...
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5
votes
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Correlation device that induces a specific transition probability
The common prior $p\in\Delta L$ and the transition probability $q:L\to\Delta A$ induce a joint distribution on $L\times A$ in which the pair $(l,a)$ is selected with probability $p_l\cdot q_l(a)$. You ...
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5
votes
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What is the game theory of retaliatory trade tariffs?
Indeed it's difficult to account for all the real-life complexities, but the basic game-theory model of trade wars is prisoner's dilemma, e.g.
https://leadersatwork.northeastern.edu/management/trump-...
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5
votes
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Sequential Game is Extensive form game?
First of all, you can differentiate between static (essentially all players move simultaneously and only once) and dynamic (essentially non-static) games.
An extensive-form game is essentially a game ...
- 5,270
2
votes
Accepted
Definition of subgame perfect Nash equilibrium
An equilibrium consists of a profile of strategies, which specifies an action for every player at each possible contingency. Since each action profile $(a_1,a_2)$ is a contingency, the SPE must ...
- 15.3k
2
votes
World as a society of interlinked multiplayer individuals
Chess is EXPTIME-Complete, which makes it significantly harder than NP-Complete problems.
Perhaps you are interested in the study of economic networks. Strategic network formation sounds like a good ...
- 1,236
2
votes
Terminology for "part" of extensive form game
A "part" of an extensive form game that is not a proper subgame because it does not start at a single node but an entire information set would be called "continuation game". This terminology is fairly ...
- 5,270
2
votes
Repeated games without a beginning and an end
What you're asking seems to me just a matter of interpretation. Note that $\mathbb Z$ and $\mathbb Z_+$ have the same cardinality. So it makes no substantive difference which index set you use.
...
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2
votes
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Pure-Strategy Bayesian Nash equilibrium with general common prior
Matrix looks correct. To final all pure strategy BNEs, you'll have to discuss cases based on the value of $p$.
For example, if $p\in(0,1)$, then $FT$ is player 2's unique best response to $F$. Thus, ...
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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
2
votes
Profit Maximizing with a competitive fringe
The question is a bit unclear to me, but I am guessing this is what we need to do.
We can think of the situation as a dynamic game where the competitive firm takes the price as given and makes a ...
- 605
2
votes
Extensive Form of Games
The extensive forms of the signalling game and the twice-repeated prisoner's dilemma have the depicted specific shapes (showing who decides what in which sequence having which information) because ...
- 6,550
2
votes
Accepted
Subgame perfect Nash equilibrium when there is a tie in payoffs seems problematic
Your analysis is correct in principle, but your notation is not. A (behavioral) strategy for a player in a perfect information game has to specify a probability distribution over actions for each ...
- 6,550
1
vote
Accepted
Relation between Markov Perfect Nash Equilibrium and Markovian evolution of the state
Q1.
Assumptions 1 and 2 are independent of one another.
Assumption 2 is an assumption of the fundamentals of the game, the setup if you will, and have no restrictions of the solutions. Its merely a ...
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Design of efficient cheap talk communication
There are some examples of this like:
Kim, Kyungmin, and Philipp Kircher. "Efficient competition through
cheap talk: the case of competing auctions." Econometrica 83.5 (2015):
Kim, Kyungmin,...
- 2,673
1
vote
1
vote
Estimation of point-identified Dynamic Discrete Choice models with moment inequalities
Function $Q$ has to be minimized wrt $(\theta,\alpha)$.
The parameters $(\theta,\alpha)$ compatible with Nash equilibrium and rationalizing (or generating) the data have to satisfy $$g(x;\theta,\alpha)...
- 3,144
1
vote
How to achieve the best outcome by a single statement in this game?
Here is a proof that the response given by Schelling in Eric’s answer is (as good as) the best A can do.
A can only do so much in retaliation for B and C teaming up against him. He can threaten to ...
- 605
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vote
How to achieve the best outcome by a single statement in this game?
Schelling himself gave an answer for Q1 in which A can achieve a surviving probability arbitrarily close to 5/6. I quote the book below. The wording is painfully tortuous at times. But the answer ...
- 131
1
vote
Accepted
Spence's Job Market Signaling Game
I don't have a copy of Gibbons handy, so I cannot speak to the specific model presented there, but only generally. The intuition of the conclusion is based on the combination of the following factors:
...
- 15.3k
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 ...
- 5,270
1
vote
SPNE and Pareto Optimality
Proof of "the SPNE of a sequential game might not necessarily be Pareto Optimal"?
I don't get it, your example is a proof of this statement. So what else do you need?
If you need another example, ...
- 355
1
vote
Accepted
Sequential Bertrand game with differentiated goods, how to write the strategies of firm 2
You have the profit function of firm 2 in terms of prices $p_1$ and $p_2$.
Then, you can find $p_2^*(p_1)$, the optimal reaction of firm 2 for any observed price $p_1$.
Firm 1 anticipates this ...
- 5,270
1
vote
Price setting firms with cost reduction technology
Your reasoning for the 1st part is correct.
The 2nd part is a 2-period game. You should try to solve it by backward induction. First you go through all the 2nd period subgames. Then you can use the ...
- 970
1
vote
Accepted
Extensive Form Games
I believe you are correct -- though I will say appealing to the one-shot deviation principle here seems a little overpowered. There are only three stages to this game so checking for all equilibria (...
- 2,156
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