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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". ...
Herr K.'s user avatar
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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 ...
Michael Greinecker's user avatar
5 votes
Accepted

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-...
against very long user names's user avatar
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 ...
Bayesian's user avatar
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4 votes

On and off equilibrium path game theory

I do not think it is standard to call equilibria on or off path. Here are the standard definitions: A path is the set of histories induced by some strategy profile (graphically, think of one ...
Wittgenstein's Poker's user avatar
2 votes
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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 ...
Herr K.'s user avatar
  • 15.4k
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 ...
ml0105's user avatar
  • 1,246
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 ...
Bayesian's user avatar
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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, ...
Herr K.'s user avatar
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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 ...
Tanay's user avatar
  • 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 ...
mynameparv's user avatar
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 ...
VARulle's user avatar
  • 6,900
2 votes
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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 ...
VARulle's user avatar
  • 6,900
1 vote
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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 ...
Walrasian Auctioneer's user avatar
1 vote

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,...
csilvia's user avatar
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1 vote

Perfect recall assumption

Perfect recall means that every player remembers her own history.
Giskard's user avatar
  • 29.2k
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)...
Bertrand's user avatar
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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 ...
H Rogers's user avatar
  • 638
1 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 ...
Eric's user avatar
  • 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: ...
Herr K.'s user avatar
  • 15.4k
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 ...
Bayesian's user avatar
  • 5,291
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, ...
Marcelo Gelati's user avatar
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 ...
Bayesian's user avatar
  • 5,291
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 ...
Tobias's user avatar
  • 970
1 vote
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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 (...
Theoretical Economist's user avatar

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