# Tagged Questions

For questions regarding the the Nash equilibrium solution concept in strategic games.

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### In a game with imperfect information, can there be no subgame-perfect equilibrium?

In our Game Theory class, we learned that games can have multiple Nash equilibria and multiple subgame-perfect Nash equilibria ($SPNE$). In one of our example problems, however, we came across a game ...
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### Why players play nash equilibria?

I have to hold a talk about pure strategy normal form games. I will explain the Nash equilibrium. I think the definition is not that hard to understand as opposed to the idea why Nash received the ...
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### Is this considered a supermodular game?

Is this considered a supermodular game? I have $\Pi_i(x_1,x_2)$ which is a submodular function with decreasing differences in $(x_1,x_2)$. I know that $-\Pi_i(x_1,x_2)$ is supermodular in its own ...
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### Equilibria in submodular games

Suppose I am solving a Cournot duopoly problem in which $U_i(x_i,x_j)$ is not for certain supermodular in its own strategy. Is the set of Nash equilibria nonempty? Can I find conditions for which the ...
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### How to solve mixed strategy Nash equilibrium.

Lets say I have following problem: Zero sum game. Payoff matrix for player one: -1 4 4 2 6 -2 I start by writing equations for each strategy. ...
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### Game theory: Finding Nash equilibrium in $3\times 3\times 3$ matrices

I tried to find how to solve $3\times 3\times 3$ matrix to find Nash equilibrium but I could not find anything on the web. Maybe I am searching with wrong keywords... I understand how to solve Nash ...
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### Difference between Sequential and Weak Sequential Equilbria

This is in reference to the Game theoretic concepts as Nash equilibrium refinements. Sequential equilibrium are often defined as satisfying two conditions: consistency and sequential rationality. ...
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### Game theory, Book by Tirole and Fudenberg, Never a weak best response,unclear example

In this book, I have the following problem: on page 446, there is a sentence: Note that $(0.9,0.9)$ is not removed by NWBR, as D is not dominated after C is deleted. I do not understand this "as". ...
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### Nash equilibrium for n players game

There is a question that I am trying to solve but I am not sure about my approach and is hoping I could get some help. Here is the question: There are $n$ companies sharing a water reservoir, let's ...
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### Gaining intuition as to why maximal lotteries use randomness to break general ties

The maximal lottery is a voting system based on choosing an optimal candidate game-theoretically. If a winner isn't clear (there is no condorcet winner), then it will return probabilities as to which ...
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### numerical solution for nash equillibrium

I have the following setup. $\pi_1=f_1(q,r)$ and $\pi_2=f_2(q,r)$ are the real valued payoff/profit functions of the two players. Player 1 gets to pick $q$ and player 2 gets to pick $r$. I also know ...
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### Nash equilibrium for two players game.

Consider a game for two players, say "Player A" and "Player B". The two sets of strategies are denoted by $A$ and $B$, available to the players. Consider a symmetric situation where the players have ...
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### Find a Nash equilibrium solver

The solvers I know so far are designed only to allow payoffs as given numbers. But is there a solver allowing users to type payoffs as variables?
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### What is the optimum strategy? Game Theory.

If you invest Rs 1000, you would get a paid back of Rs 4000 at the end of the day, provided atleast 90% of the students invested. If the number of students investing falls below 90%, all those ...