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Finding the mixed-strategy Nash equilibrium in this game

First, note that there is a lot of weak domination: $$Lr \succeq Ll, ~ Lr \succeq Rl, ~ Rr \succeq Rl, Ll \succeq Rl.$$ Consequently, $\nexists$ MSNE in which both players mix at the same time. If $...
matthewoulton's user avatar
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Gale-Shapley Follow-up Literature and General Questions

This is a very old question but I just want to add a few notes not covered in ml0105's great answer. What sort of literature has been done building off of this? ... What sort of applications does the ...
cottontail's user avatar
2 votes
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Can a mixed strategy that is strictly dominant exist if there is no strictly dominant pure strategy?

It is not possible for a mixed (non-pure) strategy to be strictly dominant. A mixed strategy can be weakly dominant, but only if all pure strategies in its support are weakly dominant. This ...
jschnei's user avatar
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Finding the normal representation of extensive form game

$$ \begin{array}{c|cccc} \text{P1} \backslash \text{P2} & \text{Ll} & \text{Lr} & \text{Rl} & \text{Rr} \\ \hline \text{T} & (3,2) & 0.9\cdot(3,2) + 0.1\cdot(1,1) & 0.9\...
Giskard's user avatar
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Finding the subgame-perfect equilibrium in sequential games with infinite action spaces

You should still use backward induction. Since the game is not finite, you should not look at the penultimate nodes corresponding to different $q_1$ quantities one by one, but rather figure out what ...
Giskard's user avatar
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1 vote
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How to judge whether NE involves a Weakly Dominated Strategy?

You are right that neither the Pareto dominance nor Weak dominance criteria apply to refine the set of Nash equilibria. To make this clearer, notice by iterated elimination of strictly dominated ...
Joseph Basford's user avatar
1 vote

How many subgames are there in this game?

P2 knows where they are, but if P3 plays afterward, they don't. To see if a subgame starts at a node, check whether any of the weakly later nodes are connected by an information set with a node that ...
Michael Greinecker's user avatar
2 votes
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Market signaling with a national exam

I think your reasoning is correct. There is no need to have an ''expected pay'' as in a separating equilibrium, everyone ''knows'' that good types will take the test and bad types will not. The only ...
tdm's user avatar
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Mixed Strategy Nash Equilibirum, Contributing to a Public Good

You could try to randomize the row. That is, let the probability of player 1 to choose 0, 1, 2 be p1, p2 and (1-p1-p2), respectively. In the equilibrium, player 2 must be indifferent to choices 0,1,2 ...
ZZZ's user avatar
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1 vote

public good contribution game theory

In this analysis, we examine a public good contribution game involving three players. Each player can choose to either contribute or not contribute to fund a streetlamp in their town. The value of ...
GuyEternal's user avatar
1 vote

About Two Methods of Computing Bayesian Equilibria

(I only parsed what you did, perhaps I did not get it.) You seem to be overcomplicating things a bit. A good starting point seems to be whether player 2 will mix or not. If not, you can see that ...
Giskard's user avatar
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