9 votes
Accepted

What does Battigalli really mean by "Players can not choose strategies, they can only choose actions."?

The idea is precisely that players do not chose actions, but only chose one action at the time at every node at which they play, based on their beliefs about the way other players and themselves will ...
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". ...
  • 14.7k
5 votes
Accepted

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 ...
5 votes
Accepted

Models for online markets with reputation system

I would suggest you start by looking at C. Dellarocas. "The Digitization of Word-of-Mouth: Promise and Challenges of Online Reputation Systems". Management Science 49 (10), October 2003, 1407-...
  • 16.6k
5 votes
Accepted

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 ...
  • 5,090
4 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-...
  • 3,748
3 votes

Multiple equilibria: which one to select?

I'm not sure I follow the logic on that equation having infinitely many solutions and steady states. In any case, in what follows are some guidelines for equilibrium selection. It depends a lot on ...
  • 10.5k
2 votes

One-shot deviation principle for infinite repeated games and dynamic programming

There is an old result in dynamic programming due to David Blackwell, according to which stationary problems allow for stationary best responses. So if you would gain by changing your behavior after a ...
2 votes
Accepted

One-shot deviation principle for infinite repeated games and dynamic programming

A deviation (one-shot or not) can certainly generate a sequence that differs from the optimal one for an arbitrary number of periods. You could treat a dynamic programming problem as a repeated game ...
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. ...
  • 14.7k
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 ...
  • 14.7k
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 ...
  • 1,216
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 ...
  • 5,090
2 votes
Accepted

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, ...
  • 14.7k
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
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 ...
  • 4,844
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 ...
1 vote

Perfect recall assumption

Perfect recall means that every player remembers her own history.
  • 27.2k
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)...
  • 2,691
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
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 ...
  • 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: ...
  • 14.7k
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

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, ...
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 ...
  • 5,090
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 ...
  • 971
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 (...
1 vote

How to verify Value Function in nonzero sum two player Differential Game?

The first panel shows the final value function after iterating 80k (!). Should probably try an implicit method. The second panel shows the evolution from frist guess to final result $v^0\to v^j$, $j=...
  • 1,529

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