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Proofs in the Appendix A of Sannikov (2007)

I have a few questions about the proofs in Appendix A of Sannikov (2007), Games with Imperfectly Observable Actions in Continuous Time. In lemma 4, when he shows the Lipschitz continuity of $H_a(w,\...
Theoretical Economist's user avatar
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Dynamic Bertrand competition when players take turns

Consider the following game: There are two players, $i\in\{1,2\}$ Time is discrete and runs to infinity during periods $t=\{1,2,\ldots\}$ At eat point in time, players have a price $p_i(t)\in\mathbb{...
Ubiquitous's user avatar
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Why is the symmetric grim trigger not a Nash?

Consider the stage game: Let $\delta\in(0,1)$ be the discount factor. Let $G$ be the symmetric grim trigger strategy profile. The payoffs are then $$E_{A}(G) = E_{B}(G) = \sum_{i=0}^{\infty}3\delta^{...
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Discount factor and deviating from strategy - Game Theory

I have an exercise in Steven Tadelis Game theory Introduction book (10.2) : Grim Trigger: Consider the infinitely repeated game with discount factor $δ < 1$ of the following variant of the Prisoner’...
Slim Shady's user avatar
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About the normal form of a repeated game

Consider an infinitely-repeated game with perfect monitoring and pure strategies. The one-shot deviation principle tells us that a strategy profile $\sigma$ is a subgame perfect Nash equilibrium if ...
Star's user avatar
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Definition of stationary subgame perfect Nash Equilibrium in a repeated game

Consider a standard $n$-players infinitely-repeated game with pure strategies. Let $\sigma_i$ be the strategy of player $i$. In particular, $\sigma_i$ maps each history $h_t$ to a pure action $a_t$ ...
Star's user avatar
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Proof of a lemma about PPE

Dear all, I am studying the repeated game with imperfect monitoring. I have so many questions about the proof of lemma 3.6 in slide 22. First of all, why we can write $$ P_{\widehat{\sigma}_{i}, \...
Maynard's user avatar