16 votes
Accepted

Why is pre-specification of punishment order necessary to manipulate compliance?

Denote the cost of the punishment by $p$, the cost of registering by $r$. In order for the plan to work, you need to have $p > r$. If the order is known, then the person at the top will choose to ...
  • 27.2k
11 votes

Why is pre-specification of punishment order necessary to manipulate compliance?

A game can have multiple Nash equilibria. You've correctly observed that, even if the punishment order isn't pre-specified, everyone registering is still a Nash equilibrium: each citizen knows that, ...
7 votes
Accepted

MWG 8.B.7 - Any strictly dominant strategy must be a pure strategy

Fix any $\sigma_{-i}$. Assume $\sigma_i$ is strictly dominant but not a pure strategy. Let $X$ be the support of $\sigma_i$. Since $\sigma_i$ strictly dominates all pure strategies $s_i\in X$, we have ...
  • 4,844
5 votes
Accepted

Why does the belief over information sets with probability zero matter in Perfect Bayesian Equilibrium?

The key is that "since both equilibria satisfy sequential rationality" is no longer true when you consider weak sequential equilibria. Both concepts satisfy sequential rationality on-path, ...
5 votes
Accepted

Correlation device that induces a specific transition probability

The common prior $p\in\Delta L$ and the transition probability $q:L\to\Delta A$ induce a joint distribution on $L\times A$ in which the pair $(l,a)$ is selected with probability $p_l\cdot q_l(a)$. You ...
5 votes

Game Theory Model needed to model the question whether "not taking the covid vaccine is free-riding"

If the question is whether not taking the covid vaccine is free-riding, then the answer is NO. In a Prisoner's Dilemma or a Public Good Game in the standard sense, free-riding (defection) is by ...
  • 4,844
4 votes

Is a Monopoly equilibrium also a Nash equilibrium?

In a somewhat degenerate way, yes. The specified demand function is a trivial case of a best response function describing the optimal quantity demanded for any given price of the monopolist. The ...
  • 479
4 votes
Accepted

Bergemann and Morris information designer and decision rule concept

Bayes Correlated Equilibrium characterizes (by Theorem 1 in the paper) what can happen in a Bayes Nash Equilibrium in which the players might have more information than is specified in the Bayesian ...
4 votes

Can a dominance solvable game have a mixed strategy equilibrium?

No, that is not possible. Assume that player $2$ has a strategy $s_{2j'}$ that is strictly dominated by $s_{2j}$. This means that for all pure strategies $s_1$ of player $1$, we have $$ f_2(s_1,s_{2j})...
  • 27.2k
4 votes
Accepted

Nash Equilibrium with Constraints on Decision Variables

Usually in (non-coopeative) game theory, one assumes that players take their actions independently. In this sense, a players' set of feasible actions should be independent of the action taken by the ...
  • 8,652
4 votes
Accepted

Level-0 in Level-k model

A Level-$0$ player is "non-strategic" in the sense that they do not take into account the possible actions of the other players. Typically, but not necessarily, a Level-$0$ player is assumed ...
  • 14.7k
3 votes
Accepted

Best response to convex combination of strategies

Here's a hint. Consider this game: \begin{array}{|c|c|c|} \hline &L&R\\\hline U&4,.&0,.\\\hline M&0,.&4,.\\\hline D&3,.&3,.\\\hline \end{array} What is player 1's best ...
  • 4,844
3 votes

Equivalence from correlated/communication equilibrium to Nash Equilibrium?

You take $p$ to be the corresponding correlated equilibrium with $A_k$ being the strategy space of player $k$ Conditions 1. and 2. mean that each player can compute the prescribed action they should ...
3 votes
Accepted

Sequential and Perfect Bayesian Equilibrium: an example?

Take the Beer and Quiche Game as an example. Let's verify that the following is a weak PBE: Both types ($S$ and $W$) of player 1 choose beer ($B$); When player 2 sees a beer choice, he believes that ...
  • 14.7k
3 votes
Accepted

How realistic is the conclusion that players do not change their mixing proportions in response to changes in their own payoffs?

I don't think the major lesson is quite that. If an expected payoff maximizing player mixes between several pure strategies, they must be indifferent between playing all of them. This has the curious ...
3 votes

Why is pre-specification of punishment order necessary to manipulate compliance?

What is wrong with this reasoning? It assumes that the cost of punishment $p$ and the cost of registering $r$ are the same for everyone, therefore it is possible to find a punishment ensuring $p>r$...
  • 139
2 votes

Bertrand competition with homogenous good and Hotelling's spatial model

Nudge: Read the paper On Hotelling's "Stability in Competition" by d'Aspremont, Gabszewicz and Thisse.
  • 27.2k
2 votes

Nash equilibrium in strictly mixed strategies

Nash's theorem says that every finite game has a NE in mixed strategies, but here mixed, coming without the qualifier strictly, implies the weak version that includes pure strategies. So your ...
  • 4,844
2 votes
Accepted

Subgame perfect Nash equilibrium when there is a tie in payoffs seems problematic

Your analysis is correct in principle, but your notation is not. A (behavioral) strategy for a player in a perfect information game has to specify a probability distribution over actions for each ...
  • 4,844
2 votes

How can we prove that an equilibrium in dominant strategies is a Nash equilibrium?

Your intuition about the proof is correct indeed. A more formal proof would involve examining the definitions of dominant strategy and Nash equilibrium: A strategy $s_i^d$ is a dominant strategy for ...
  • 14.7k
1 vote

(Game Theory) Why is voting for your worst alternative a weakly dominated action?

To see that voting $C$ for a type $A$ voter is weakly dominated you need to find a strategy that results in a weakly better outcome irrespective of the behavior of the other voters. Voting $A$ would ...
1 vote
Accepted

Convex Preference in Nash Equilibrium

Convexity (quasi-concavity) of preferences is important for both Nash Eq and exitence of general equilibrium. Without this assumption, the best response correspondences are not necessarily convex ...
  • 8,652
1 vote
Accepted

What does it mean when an economist talks about "equilibrium"

There are multiple notions of what equilibrium is when it comes to economics although they are all related. There is a paper fully dedicated to this topic by Backhouse (2004). Following Robinson (1956:...
  • 45.1k
1 vote

What does it mean when an economist talks about "equilibrium"

The general idea of equilibrium is borrowed from physics: An equilibrium is a state of a given system such that all forces acting on it are counterbalanced and the state therefore doesn't change on ...
  • 4,844
1 vote

Strategic game with complete informaation

The given solution is as follows: Suppose $a_1 < a_3$. Straightforward argument shows that the set of actions that constitute pure best response for player 2 is $\{1, . . . , a_1\}$. When $a_1 > ...
1 vote

Price competition; finding the equilibrium expression for price and profit

I didn't work out the algebra, but you are on the right track. The thing to remember is that for the Nash equilibrium, each player chooses a strategy (in this case choosing price) and maximizes ...
  • 46

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