Questions tagged [nash-equilibrium]

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3 votes
0 answers
124 views

Poker with infinite stack size

In two-player No Limit Texas Hold 'Em (NLHE), the optimal strategy depends on the "effective stack size," that is maximum amount of money held by one of the players (in the sequel I'll just ...
3 votes
2 answers
140 views

Existence of stationary Nash equilibrium of discounted stochastic game

$N$-player discounted stochastic games with finite state and action spaces possess a Nash equilibrium in stationary strategies. This has been proved by Fink (1964) and a closely related result by ...
1 vote
0 answers
37 views

Nash Equilibria change linearly in (some) game parameters. Already known / follows from a more general result?

EDIT: The key thing that I am wondering about is the linearity of the P2 strategy, not the constancy of P1. (The latter is straightforward.) Question: Is the following result already known? Or is it a ...
2 votes
1 answer
190 views

Nash equilibrium at another level

This is a variant of the Nash equilibrium. Let's say that there are 3 prizes: A Ferrari, a diamond watch, and a new boat. There are 6 players. 3 players with a motive while 3 players with another ...
2 votes
0 answers
70 views

Equilibrium for a game with mixed strategies on a compact ultrametric space

Let $(X,d)$ be a compact ultrametric space. Hartig and de Vink considered the following ultrametric on the set $P(X)$ of probability on $X$: $$\hat d(\mu,\nu)=\inf\{r>0:\forall x\in X\;\;\mu(B_r(x))...
-1 votes
1 answer
140 views

Why do two potentials of a game only differ by a constant? [closed]

Can someone explain to me the proof on page 7/20 of the original paper about potential games (https://www.cs.tau.ac.il/~mansour/sem-game-02-03/monderer-potential-96.pdf)? It is about why two ...
-1 votes
1 answer
319 views

Proving the existence of a symmetric Bayesian Nash equilibrium

I am currently faced with the following question: Consider the public goods game. Suppose that there are $I > 2$ players and that the public goods is supplied (with benefit of 1 for all players) ...
2 votes
0 answers
120 views

Existence and uniqueness of solution of a nonlinear system

I need a proof of the following result to calculate a Nash equilibrium in the Showcase Showdown game. For all $n>1$, the system of equations $$\left\{ \begin{aligned} (1+e^{x}(-1+x))^{n-2}&=\...
1 vote
0 answers
201 views

Nash equilibrium as the number of players goes to infinity

I'm trying to find results that characterize the Nash equilibrium in a multi-player game as the number of players $N$ goes to infinity. The game could be symmetrical, or maybe there could be a ...
1 vote
2 answers
240 views

Should mixed strategies in normal form games be interpreted as measurable functions or probability vectors?

I have recently been stuck trying to understand how game theorists extend a normal form game (matrix game) into a game with mixed strategies (so called mixed extension). I feel like I am missing ...
0 votes
2 answers
172 views

Help with a definition of a two-person game in a referenced paper

In the paper "Finding Mixed Nash Equilibria of Generative Adversarial Networks" the authors write in equation (1) on page 2: Consider the classical formulation of a two-player game with finitely ...
16 votes
2 answers
13k views

Simple proof of the existence of Nash equilibria for 2-person games?

Is there a nice elementary proof of the existence of Nash equilibria for 2-person games? Here's the theorem I have in mind. Suppose $A$ and $B$ are $m \times n$ matrices of real numbers. Say a ...
3 votes
0 answers
175 views

General way to find Nash equilibrium in continuous game

I'm really interesting how to find Nash equilibrium in a continuous game with two players in the general case. Let's consider a game with continuous utility functions $F_1, F_2 : [0, 1] \times [0, 1]...
1 vote
2 answers
131 views

Strong Nash Equilibria in repeated games

Suppose we have a simultaneous game, that has a strong Nash equilibrium (SNA), i.e. a weak Pareto efficient Nash equilibrium (no deviation of any subset of player brings a benefit to them). Now ...
2 votes
1 answer
37 views

On the limit of assessments that are not sequentially rational

I have asked this question in Mathematics StackExchange, but there is no response yet. I've just realized that here is the right forum for asking research level questions... :'( In game theory, in ...
1 vote
1 answer
89 views

Effective way to find Nash equilibrium

Is there any good algorithm for finding Nash equilibrium point, for one and repeated game theory? Thansk a lot for giving me some guidance.
1 vote
1 answer
323 views

Completely mixed Nash equilibrium points

Must an isolated completely mixed Nash equilibrium (i.e., all strategies for all players receive positive weight) be essential? (By essential, I mean the equilibrium z of the game G that for every ...
7 votes
2 answers
1k views

Boundedness of solutions of a difference equation

Is there someone who can show me how I can prove this conjecture? Or at least show me how to do the first implication ? Conjecture: Assume $\alpha,\beta, \lambda \in [0,\infty)$. Then every ...
6 votes
1 answer
394 views

for which values of $\theta$ does this equation $x_{n+1}=\cos(\theta)x^2_{n}-\sin(\theta)x^2_{n-1}$ have bounded solutions?

I would like to investigate the global behavior of the following equation : $$x_{n+1}=Ax^2_{n}-Bx^2_{n-1}$$ where $A(\theta)= \cos(\theta)$ and $B(\theta) =\sin(\theta)$ are nonnegative parameters ...
4 votes
2 answers
397 views

(linear algebra) - Can a symmetric equilibrium achive higher social-welfare than some equilibrium with the same support?

EDIT: rewritting the question to linear algebra to make it more accessible. Denote by $\Delta([n])$ the set of all probability distributions over $\{1,2,\ldots,n\}$, that is: $$\Delta([n])=\{x\in[0,...
2 votes
1 answer
186 views

Is there always a symmetric "subset equilibrium" for an equilibrium in a symmetric game?

Consider a 2-player symmetric game given by a payoff matrix $A\in [0,1]^{n,n}$ for the row player (i.e. the column player matrix is $A^t$). Let $s=<s_1,s_2>$ be a (possibly mixed-strategies, ...
1 vote
0 answers
358 views

What is known about multiplayer poker with flop?

I am interested in the following simplified version of poker. Each player gets a card (for example, either A or B). Then they bet knowing their own cards (for example, the pot initially has 1 euro, ...