Questions tagged [dominant-strategy]

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2 votes
1 answer
64 views

Can game theoretic concepts be applied to any groups of strategies collectively partitioning the strategy space?

It is clear that players of a game can almost always create trivial variations on strategies without breaking game theoretic conclusions. For example, a player playing Rock Paper Scissors can play ...
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0 votes
1 answer
27 views

Does Dominant Strategy Incentive Compatibility apply to this modification of Rock Paper Scissors?

I understand the notion of Dominant Strategy Incentive Compatibility in auctions. I am wondering whether this concept can be extended to all games. For example, the game "Rock Paper Scissors&...
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1 answer
42 views

Why is Dominant-Strategy Incentive Compatibility treated as a virtue, and are there mechanism design models which treat it as undesirable?

Why is Dominant-Strategy Incentive Compatibility treated as such a ubiquitous virtue? In this lecture, the answer given from the perspective of a non-principal player is, "it's easy to play; you ...
  • 379
0 votes
0 answers
26 views

Maxmin Strategy cannot be Weakly Dominated

This is homework. Question: Suppose, $\sigma_i^*$ is a max-min strategy of player $i$. Prove that if $s_i \in \operatorname{supp}(\sigma_i^*)$, then $s_i$ cannot be weakly dominated by any pure/mixed ...
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1 vote
1 answer
160 views

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

So far I have that an equilibrium in dominant strategies is one where two strictly dominant strategy profiles meet (e.g. to report the other prisoner in the Prisoner's Dilemma). Going by the ...
0 votes
1 answer
110 views

The concept of 'truthfulness' and 'indirect' in mechanism design

I'm a beginner in mechanism design. I learned that 'a (direct) mechanism is truthful if an agent truthfully reveals his/her type.' Then, how can we define a truthful indirect mechanism? I'm not sure ...
0 votes
2 answers
112 views

Nash equilibrium in strictly mixed strategies

I have the following statement which I have been said it is false, but I don't understand why: "All finite games have at least one Nash equilibrium in strictly mixed strategies, as long as there ...
0 votes
1 answer
79 views

Strategic game with complete informaation

Consider the following strategic game with complete information played by three players. Each player $i ∈ {1, 2, 3}$ chooses her action from $A = \{1, 2, . . . , 10\}$. Utility functions, mapping each ...
1 vote
1 answer
801 views

Differences between best response, dominant strategy and Nash equilibrium

I can't seem to get the differences of these terms. I watched this video that has the differences of best response and Nash equilibrium: But then I heard about dominant strategies from another video ...
1 vote
1 answer
307 views

Rationalizable strategies and Weak Dominance

Can I find the rationalizable strategies for a game where none of the players has strict dominance but only weak dominance?
1 vote
1 answer
619 views

Game with an equilibrium in pure, but none in mixed strategies?

I came across the following game: The question is to find potential equilibria in mixed and pure strategies. The solution says that there is an equilibrium in pure strategies (B,N), but none in mixed ...
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2 votes
1 answer
644 views

Set of rationalizable strategies for this 4 x 4 matrix

I would like to find the set of rationalizable strategies for this 4x4 game: The first thing I did was try and find all PSNE. I found two, the ones I bolded. Thus, my answer to this question is that ...
2 votes
1 answer
56 views

Find value of $\beta$ for which there is a strictly dominant strategy

The question is as such: $N$ firms are lobbying for subsidies. Let $h_i$ be the number of hours spent by form $i$ for lobbying, with cost $wh_i^2$ where $w$ is a fixed constant. The subsidies granted ...
0 votes
1 answer
58 views

Is it possible to find a nash equilibrium that is not an equilibrium in weakly dominant strategy?

I know that it is possible to have a Nash equilibrium which is not an equilibrium in dominant strategy, but is it also applicable for equilibrium in weakly dominant strategy (i.e. a Nash equilibrium ...
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5 votes
3 answers
2k views

Is a mixed strategy ever the best response to a pure strategy?

Suppose you are playing a game against an opponent whom you know only uses pure strategies. My question is, is there any such game in which using a mixed strategy in response is better than all the ...
0 votes
0 answers
67 views

Argue that no further mixed Nash Equilibria can exists

I'm looking at the following Normal-Form Game: ...
0 votes
1 answer
51 views

Fill out Normal-Form Game to obtain exactly one mixed equilibrium

I'm given the following incomplete Normal-Form Game: | L | R +-------- O|1,?|7,? U|?,2|?,1 First I was asked to fill out the missing pieces to obtain a game ...
0 votes
1 answer
28 views

Illustrating difficulty to find dominant strategies: series of simple one-shot two-players games

For a game theory class I am prepping, I am looking for simple mathematical puzzles that can easily be presented as one-shot 2-players simultaneous games in which one of the players has a dominant ...
0 votes
2 answers
120 views

Are there strictly dominated strategies?

Two players simultaneously announce a prime number less than 20.Denoting $p_{i}$ the number announced by the player $i$, the payoffs are: -If $p_{1}+p_{2}<14$ each player receives as payment the ...
3 votes
1 answer
56 views

Rationalizable action profiles in nice symmetric games

Suppose we have a nice symmetric game with $n$ players, i.e. each player's action space is the same compact interval of the real line. I am tasked with identifying all of the rationalizable action ...
2 votes
1 answer
35 views

Term for the phenomenon when an undesirable but competitive strategy dominates

For example, in some sports, the use performance enhancing drugs is considered undesirable, but it is difficult or impossible to be competitive unless you use performance enhancing drugs. So, the use ...
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1 vote
1 answer
64 views

Is this market monopoly or duopoly?

Could you help me to identify monopoly, because I got confused. There is a company with market share of 54 %. The second one has market share of 21 %. Can this market be characterized as monopoly or ...
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2 votes
1 answer
125 views

Incentive compatibility: Weakly dominant strategy versus Nash equilibrium?

When it comes to proving that a mechanism e.g. auction is incentive compatible this is the approach I'm using: I break down all the cases that might happen if the agent reports an untruthful value to ...
1 vote
2 answers
313 views

Derivation of Equilibrium Strategy in 1st-price Auction?

Hey, everyone. I desperately need help understanding some math in auction theory. I have been writing a paper as an undergrad for auction theory, and after all of my research I just cannot understand ...
1 vote
2 answers
2k views

Nash Equilibrium and Dominant Strategy

If I have a game that goes as follow: Player 1 is the row player and player 2 is the column player. I think that the Nash Equilibria should be (10, 5) and (5, 10), since neither of the player has ...
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1 vote
0 answers
27 views

Reference for truthful Nash on cartesian domain implies strategy-proofness

Consider a mechanism $M: \mathcal{R} \rightarrow X$, where $\mathcal{R}$ is a domain of preference profiles $R = (R_1,\dots, R_n)$, and $X$ is a set of outcomes. I believe that the following is a ...