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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6
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2answers
48 views

Why is infinite recursion on the common knowledge assumption necessary?

If something is common knowledge in a game, that means that every player knows it, and every player knows that every player knows it, and so on. Are there cases where only one such level of knowing ...
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1answer
23 views

REE with asymmetric information and Bayesian Nash equilibrium?

What is the difference between a Rational Expectations Equilibrium (REE) with asymmetric information and Bayesian Nash Equilibrium (BNE)? Since agents in both cases play some game or have a strategic ...
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1answer
40 views

How to find mixed optimal strategies in this zero-sum game?

I'm trying to solve this problem from last year final exam in game theory: Consider the zero-sum game $G=(X, Y, g)$ where $X=Y=[0,1]$, and $$\forall (x,y) \in X \times Y: g(x, y)=\max \{x(1-2 y), y(...
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0answers
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Who is the first person/paper to introduce “mixed strategy”?

Who is the first person/paper to introduce "mixed strategy"? The PNAS by Nash used this notion without citing anyone. Does the earlier book: Von Neumann, J., and Morgenstern, O., The Theory of Games ...
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1answer
70 views

Finding Bayesian Nash Equilibrium

I'm recently new to Game Theory and I've recently started teaching myself about Bayesian Nash Equilibirum. I've stumbled across a problem set that I can't seem to wrap my head around concerning ...
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1answer
25 views

How would a 2D model of Hotelling's law outweigh the benefits of a 1D model?

I'm not sure if this goes here, or on a math exchange. I could move it if you guys want... Let's examine Hotelling's law on a 1D plain with two shops. Both shops would do society a favour if placed ...
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1answer
87 views

Confusion about the convexity of the best response correspondence

I am recently reading the proof of the existence of the Nash Equilibrium. As a math student, I do understand the use of Berge's maximum theorem and Kakutani's fixed point theorem, but I am not sure ...
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1answer
26 views

Is it possible to find a nash equilibrium that is not an equilibrium in weakly dominant strategy?

I know that it is possible to have a Nash equilibrium which is not an equilibrium in dominant strategy, but is it also applicable for equilibrium in weakly dominant strategy (i.e. a Nash equilibrium ...
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1answer
30 views

Difference between equilibrium and k-rationalizability

I'm reading a Structural Models of Nonequilibrium Strategic Thinking: Theory, Evidence, and Applications by Crawford, Costa-Gomes and Iriberri. They write the following: In two-person games, a ...
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1answer
21 views

How to read nash equilibrium from a normal form?

For example, on the section with the title "sequential games in normal form" of this wikipedia page, there is a table with all its SPNE and nash equilibrium labelled. How are the NEs obtained? It ...
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3answers
965 views

Is a mixed strategy ever the best response to a pure strategy?

Suppose you are playing a game against an opponent whom you know only uses pure strategies. My question is, is there any such game in which using a mixed strategy in response is better than all the ...
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0answers
52 views

Existence of symmetric trembling hand perfect equilibria

Consider symmetric and finite game. By Nash (1950), the game must have at least one symmetric equilibrium (proof). Also, it must have at least one trembling hand perfect equilibrium (proof). ...
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Evolutionary stable strategies

I am new to evolutionary game theory so I can't figure out whether I'm looking at things correctly. I have the following payoff matrix: $$ A = \begin{matrix} 3 & 0 \\ 5 & 1 \end{matrix} $$ ...
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2answers
113 views

Bertrand Duopoly Equilibrium for Discrete Prices

There are two identical firms, $1$ and $2$, with zero marginal costs. They produce homogenous product, which is demanded by a unit mass of identical consumers, each of which has inelastic unit demand ...
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51 views

Unique Nash-equilibria in multi-unit auctions with uncertain participation

Setup Consider a one shot sealed bid multi-unit auction where $N$ bidders compete for $K$ identical objects and each bidder $i$ has demand $d_i\in \{1,\dots,K\}$. Bidders receive private i.i.d. ...
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1answer
60 views

Trembling hand perfection and weakly dominated strategies

It is well known that players cannot use weakly dominated strategies in a trembling hand perfect equilibrium. My question, however, is a little different: does iterated deletion of weakly dominated ...
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1answer
39 views

Incomplete information in multi stage game

I would like to solve a game where firms have private information about their own type, but only know the distribution of the other firm's type. They interact in two stages, where the strategies ...
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0answers
26 views

Argue that no further mixed Nash Equilibria can exists

I'm looking at the following Normal-Form Game: ...
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1answer
36 views

Fill out Normal-Form Game to obtain exactly one mixed equilibrium

I'm given the following incomplete Normal-Form Game: | L | R +-------- O|1,?|7,? U|?,2|?,1 First I was asked to fill out the missing pieces to obtain a game ...
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1answer
90 views

Difference between Nash equilibrium and Pareto Efficiency

Nash Equilibrium is defined as a solution concept referring to a best outcome which players won't want to unilaterally deviate given the response of other players doesn't change. To me it seems like ...
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1answer
35 views

Non-Bayesian Mechanism Design

Suppose we have a mechanism where a finite number of agents possess private information that is not drawn from a probability distribution. The agents' types are given and fixed but agents only know ...
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3answers
69 views

Maximum-support Nash equilibria in zero-sum games

Context: I would like to know how likely a player is to pick a specific action, provided that he plays optimally and the action is optimal. Phrased like this, the question is ill-defined. But is there ...
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1answer
28 views

I cannot find for this Simple shared effort level game

Each player can contribute to the project with non-negative effort. Player 1's utility is $u_1=e_1(1+e_2-s\cdot e_1)$ where $s\in [0,1]$. Player 2's utility is $u_2=e_2(1+e_1-e_2)$ For case 1, ...
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1answer
180 views

The difference between a Nash equilibrium and Bayesian Nash equilibrium [closed]

What is the basic difference between Nash equilibrium and Bayesian equilibrium?
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1answer
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Fehr & Schmidt, ultimatum game, inequaltiy aversion, perfect subgame Nash equilibrium

I am preparing for an exam. I have found an old exam but I have no solutions for it, so I tried to solve it, but I dont know if I did it correctly and need therefore your help. The problem looks as ...
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1answer
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NASH equilibrium [closed]

How to approach questions like these: In a two player static game with a discrete strategic space that permits each player to chose one of the four possible strategies what is the maximum number of ...
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0answers
26 views

Optimal pareto in two-person game

For what values $x$, $y$ the profile $(D,L)$ is Pareto optimal? \begin{array}{c|ccc} & L & R \\ \hline U & x,5 & x+2,y \\ D& 1,-1 & x,0 \\ \end{array} Is correct $x<1$ ? ...
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27 views

Condition for a Nash equilibrium

Consider two people have a mutually advantageous relationship. That is, if both dedicate more effort to the relationship both improve. Specifically, each individual chooses a level of effort $x_{i}\...
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0answers
36 views

Asymmetric Nash Bargaining

The Nash bargaining solution selects the unique solution to the maximization problem $\max_{s_1, s_2 } (s_1 - d_1) (s_2 - d_2)$ such that the solution satisfy the following axioms : Invariance ...
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1answer
25 views

Rationalizability or Nash equilibrium

In the 'chicken' game, (stop,go) and (go, stop) are the two pure strategy Nash equilibrium profiles. If the game is played once, does it make more sense to use the rationalizability solution concept? ...
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1answer
34 views

Interpretation of Solution Concepts

I was wondering whether there is a neat overview over different interpretations of game theoretic solution concepts such as Nash equilibrium, Sequential Equilibrium and the like. Textbooks I found ...
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2answers
78 views

Game Theory: finding nash equilibria of an extensive form game (game tree) [duplicate]

How do you find the pure Nash equilibria from this commitment game? The SPNE is (U, ps) Do you find the NE by finding the best response (BR) of a player to a specific strategy of the other player? ...
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1answer
171 views

Definition of Bayesian Nash equilibrium

I have a basic doubt on the definition of Bayesian Nash equilibrium. Consider the following game: 1) $N$ players. 2) Each player $i$ has a type, assigned by nature and denoted by $\epsilon_i$. ...
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1answer
82 views

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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1answer
184 views

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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54 views

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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42 views

How to find nash equilibrium in this model? [duplicate]

I am only looking for an intuitive answer, so I won't provide any specific equations. In this model: firm A and firm B compete on prices. Firm A is always better off choosing a smaller price than ...
3
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2answers
60 views

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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1answer
174 views

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 ...
3
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1answer
40 views

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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2answers
58 views

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 ...
3
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1answer
54 views

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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1answer
44 views

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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0answers
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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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0answers
16 views

Finding correlated equilibria

I am a bit confused in my game theory class when it comes to finding correlated equilibria. I understand how to write the constraints using probability distributions, but I don't know how to find the ...
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1answer
116 views

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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1answer
114 views

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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0answers
70 views

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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1answer
64 views

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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1answer
124 views

Static game with complete but imperfect information

I am confused on the concept of static game with complete but imperfect information and its consequences on the equilibrium definition. Suppose we have 2 players. Each player $i$ chooses action $Y_i\...