# Questions tagged [nash-equilibrium]

A basic solution concept in game theory that requires each player to select their best response to the strategies chosen by others.

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### Repeated Game SPNE

I approached this question in this way: $(P_1,P_2), (R_1,R_2), (S_1,S_2)$ are the Nash Equilibria of the Stage 1 game. For the given strategy to be sustained as SPNE, there should be no way unilateral ...
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### Nash equilibrium - mistake in proof of paper?

I have a question regarding the proof of Proposition 1 in Besley and Ghatak (2007) in Appendix A of their paper. It is a quite highly cited paper but I believe there is a mistake in the proof of their ...
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### Cournot competition subgame perfect Nash equilibrium with two products

QUESTION: Assume there are two types of products, labelled $l$ and $n$. Firms compete in the market by choosing which product to sell and then choosing the quantities. Let $Q_n$ and $Q_l$ denote the ...
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### What trick can be used to calculate mixed-equilibria?

In continuous games, the probability distributions over the players' strategy spaces are infinite. How then is it even possible to then derive a mixed-strategy nash equilibrium? One would have to ...
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### Sequential Bertrand game with differentiated goods, how to write the strategies of firm 2 [closed]

In a Bertrand competition with differentiated goods where firms set the prices sequentially, we have the following demand functions: q1 is quantity of goods demanded for firm 1 q2 is quantity of ...
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### Rationalizable action profiles in nice symmetric games

Suppose we have a nice symmetric game with $n$ players, i.e. each player's action space is the same compact interval of the real line. I am tasked with identifying all of the rationalizable action ...
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### What does these “strategy notations” mean?

In a sequential game, where there are 8 pizzas. Player 1 decides number of pizzas he wants. Let's call it S1 (strategy of player 1), and S1 = 5 means player one decided to get 5 pizzas. Then player ...
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### Necessary indifference conditions in mixed equilibrium

Suppose we are playing a game where the Action set for Player 1 is $(a,b)$, for Player 2 is $(c,d)$, and for Player 3 is $(L,M,R)$. Assume that for Player 3, the action $M$ is weakly dominated by some ...
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### Non-negative deviations from Nash Equilibrium

I know that in a Nash Equilibrium, no player can profitably deviate from the equilibrium strategy assuming that the strategies of the other players remain the same. My question is, what if a player ...
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### Take It Or Leave It Strategy: Social Optimum

Here is what I understood Using Backward Induction, I inferred that buyer offers a price, say, $P$ and the seller will sell only if $P \geq c(I)$. Setting the lowest possible Price that will ensure ...
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### Disagreement in Strategic Bargaining

Construct a pair of startegies for the ultimatum game ($T=1$ bargaining game), that constitutes a Nash Equilibrium and together support the outcome that there is no agreement reached by the two ...
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### Computing pure strategy Nash equilibria in finite games

I am trying to compute the (pure strategy) Nash equilibria of some discrete auctions. More precisely, let us define the strategy of each player as a function mapping from every valuation that they ...
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### Prisoner's dilemma as a Bayesian one-shot game

What happens if we assume that there is incomplete information to the prisoner's dilemma game? For example, suppose we have the following matrix with the utilities $T>R>P>S$ and $2R>S+T$ ...
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### Solving a two stage game by backward induction: which is the equilibrium notion?

Take a two-stage game with complete information and simultaneous actions in each state: (1) Player 1 and 2 simultaneously choose action $a_1\in A_1$ and $a_2\in A_2$ respectively. (2) Player 1 and ...
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### Existence of nash equilibria in finite games

I was going through the proof of existence of a Nash Equilibria in finite normal form games (Proof via Brouwer’s theorem) and got a question regarding the requirement of finiteness for the number of ...
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### Example of a game with no Nash equilibria but at least one correlated equilibrium

In this answer there is the offhand remark Of course, a game with no Nash equilibria may have a correlated equilibrium, but I'm not aware of any simple examples where this is the case. Can ...
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### Nash Equilibrium in 2 bidder auction

I am trying to find Nash Equilibrium of an auction with two bidders in which the highest bidder wins the object but both bidders pay the losing bid. Here every bidder follows the same bidding strategy ...
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### Rosen's unique equilibrium conditions: Multi dimensional strategies?

I was wondering if the uniqueness of equilibrium conditions in n-person games as published in Rosen's 1965 paper (J. B. Rosen. Existence and uniqueness of equilibrium points for concave n-person games....
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### Bertrand-equilibrium with discrete price set

Consider a market for a homogenous product with three producers, firms A, B and C. The firms have constant marginal costs which are equal to $c = 20$ for each firm. Consumers always buy from the firrm ...
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### Non-cooperative Nash Equilibrium in political game

I have difficulties deriving the non-cooperative Nash Equilibrium of this problem. The objective function is to maximize the expected total rent over the two periods, that is: \begin{align} \max_{...
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### Can a game with a unique pure strategy Nash equilibrium also have a mixed strategy equilibria?

Consider an arbitrary 2x2 simultaneous game with complete information. Say that the model has only one pure-strategy Nash equilibrium. For example (first pay-off refers to Player 1): ...
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### Existence of pure strategy Nash equilibrium

I understand the reason why mixed strategy Nash equilibrium exists. But what are the conditions for the existence of pure strategy Nash equilibrium?
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### How to demonstrate that a game always have a subgame-perfect equilibrium in pure strategies?

If I have an specific extensive game, with only a finite set of strategies, how can I demonstrate that the game always have a subgame-perfect equilibrium in pure strategies? My first intuition was to ...
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### Zero sum game, constant sum game

Given any bilateral zero-sum game G, show that strategy proﬁle σ is a Nash equilibrium for G if, and only if, it is a Nash equilibrium for the constant-sum game G' obtained from G by adding any ﬁxed ...