# Tag Info

9

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 play at future nodes in the game (where beliefs are conditional on the history that led to that node). The interpretation is letting players choose full-...

5

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, 1407-1424. for a review of relevant literature and Friedman & Resnick "The Social Cost of Cheap Pseudonyms". Journal of Economcs and Management Strategy. 10 ...

5

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 tree. This form of presentation makes sense when looking at games where players move sequentially. However, you could also represent a simultaneous-move game ...

4

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-tariffs-and-the-prisoners-dilemma/ The concept of the Prisoner’s Dilemma is important to a number of business school subjects, including economics and ...

3

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 the context. Here are some criteria, in descending order of relevance Clean Ways Is any of the steady states unstable? If so, it's less likely to be the one ...

2

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 certain history, you would gain by changing it at every history corresponding to the same state. For the original reference, see the corollary to Theorem 1 ...

2

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 between one player and chance. The one-shot deviation principle should then carry over from repeated games to dynamic programming.

2

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. Moreover, in a continuation game with finite history, any strategy can be interpreted as a (possibly non-stationary) Markov strategy in a continuation game with ...

2

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 include functions $a^*_3(a_1,a_2), a^*_4(a_1,a_2)$ that specifies what to do at those contingencies.

2

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 starting point. A lot of the work examines when certain classes of graphs arise under pure strategy Nash equilibria. There are exponentially many pure ...

2

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 standard (Perfect Bayesian Equilibrium). However, I think what you are after is a stochastic game which consists of several states. Each state corresponds to ...

2

The best way to visualise what's going on would be to use Harsanyi's transformation. I'm not drawing the game tree here (but I think Tirole has it in his example). Let's set up notations first. We will denote player 1's strategy by $x=Pr(T)$. We will call the decision of player 2 following the realisation of game $i$ by $y_i=Pr(T)$ - i.e. player 2, following ...

2

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, to have a BNE, you'd want $F$ to be player 1's best response to $FT$ as well, meaning that you'd require $3p>1-p$, or $p>\frac14$. Hence, $(F,FT)$ is a BNE ...

1

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 $$g(x;\theta,\alpha)\leq0.$$ In the case where, for given $x$, $$g(x;\theta,\alpha)>0,$$ the parameter values have to be changed in order to possibly reverse the strict ...

1

A caveat, this is not really an answer, more of an extended comment--that's why I've put it as community wiki. This is a cool game, one of commitment. I'll try to formalize the problem. This is a first pass, so people should edit as they see fit. It's probably easiest to solve the case where, $T$, the number of rounds before a forced execution is $1$. Let ...

1

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: Whenever the firm can tell the high and low types apart, it's willing to pay a high wage to high type and a low wage to low type If the firm cannot tell the ...

1

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 the penultimate period, and so on. Here, there are multiple NE so that the different NE can be used to reward and punish previous behavior. Your idea of how to ...

1

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, just take the prisoner's dilemma, and turn into a sequential game with imperfect information. Then, the NE is equal to the SPNE and you have an equilibrium without ...

1

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 reaction. So you can plug $p_2^*(p_1)$ into the profit function of firm 1 and maximize it with respect to $p_1$.

1

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 payoffs of the subgames and write up the investment decision subgame as a bimatrix game. However, the question is poorly written and as stated this game has no ...

1

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 (and not just your conjectured one) in each proper subgame is doable. You do seem to be applying it correctly, however!

1

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 $v^0\to v^j$, $j=80k$. Third panel is the distance between the value functions and fourth shows the error. Note that the value function is convex-concave. This is due to the ...

1

After searching for a while, this is the best answer I can so far come up with. 1) A formalized argument for why identification could break down under BBL is from Srisuma ('13). He gives two specific examples in the online appendix where identification is lost because of using additive rather than multiplicative perturbations to construct off-equilibrium ...

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