# Tag Info

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### Has the Nash Equilibrium led to any significant economic discoveries?

Two areas that have been profoundly affected by game theoretic research stemming from Nash's contribution are Oligopoly theory There are actually a few examples of what would come to be known as ...

### Has the Nash Equilibrium led to any significant economic discoveries?

You're not alone in your skepticism of the relevance of game theory. Some of the greats, including Gary Becker, were at times dismissive of the practical/empirical importance of game theory (see the ...

### Has the Nash Equilibrium led to any significant economic discoveries?

This is only half a joke : Nash-equilibrium gives a very good prediction on the relative size of groups of foraging ducks on a pond when two food sources are established at opposite sides of the pond....

### Difference between Sequential and Weak Sequential (Weak Perfect Bayesian) Equilibria?

Let's review the definitions of the two concepts. Let $\sigma$ be a profile of strategies and $\mu$ a system of beliefs. A pair $(\sigma,\mu)$ is a weak perfect Bayesian equilibrium (WPBE) if ...
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### Comparing Nash equilibria

Yes there absolutely is. It is generally agreed upon that utility is (at least) ordinal. That means I can compare utility levels for a single person (not necessarily across people) and the numbers ...
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### Rosen's Diagonal Strict Concavity condition

The diagonally strict concavity property is better known as the strict monotonicity property of the pseudo-gradient. An operator $\Psi:\mathbb{R}^n \to \mathbb{R}^n$ is strictly monotone if the ...

### Rosen's Diagonal Strict Concavity condition

So you want to find a maximum of $\sigma(s,z)$. If $\sigma$ is diagonally strictly concave you can do so by starting at any point and just following the gradient $g(s,z)$ until you find the maximum ...

### Is a Nash equilibrium anything more than what it is?

The conventional definition of Bayesian Nash equilibrium (BNE) is as follows: A pure strategy BNE is a profile of type-contingent strategies (s_i(\theta_i),s_{-i}(\theta_{-i}))=(s_1(\theta_1),\...
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A leader-leader Stackelberg is a situation in the Stackelberg model where both firms believe they are leaders. This leads to global production being much higher than expected by both firms, as they ...

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### Game theory software

I have used gambit (python) in the past and could recommend it. It also includes a small GUI which makes things very intuitive. R also has GameTheory if you prefer this platform instead
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### Bayesian-Nash equilibrium in a first-price auction

It is actually assumed that $b_i(v_i)$ is of the form $\alpha_i+\beta_i \cdot v_i$. So it is an affine function. Linearity only works if the bottom of the uniform distribution is 0. A somewhat ...
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### Example of a game with no Nash equilibria but at least one correlated equilibrium

There are three players, 1,2,3, and the action spaces of players 1 and 2 are both $[0,1]\times\mathbb{N}$, the action space of player 3 is $[0,1]$. The generic action of player 1 is written as $(x,m)$,...

### Interpretation of Solution Concepts

One reason why there exists no ultimate overview is that these issues are still under debate. A great entry point would be the survey "Foundations of Strategic Equilibrium" by John Hillas and Elon ...
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### Existence of Symmetric Pure Strategy Equilibrium

There is no guarantee that symmetric games have symmetric equilibria. See this paper for concrete examples. There is also no guarantee that symmetric games have pure-strategy equilibria. For example, ...
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### In a game with alternating moves and complete information, the Nash equilibrium cannot be a non-trivial mixed equilibrium?

As is clear from the answer of VARulle, complete information is of no use. Every (finite) game in normal-form is the normal form of an extensive form game of complete information. The situation is ...
A couple hints. Regarding the lower bound on $\epsilon$: What happens if deviation occurs at stage $T$? In other words, there is no opportunity for your so-called "punishment stages". ...