Questions tagged [dominant-strategy]
The dominant-strategy tag has no usage guidance.
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Understanding the notations in Bayesian game definition
I am having trouble understanding the definition of a Bayesian game based on the following definition from class. I would appreciate it if you could explain the notations and overall meaning for point ...
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Truthful assignment for facility allocation problems
We have the following congestion game. $n$ agents and $m$ facilities are positioned on the real line $\mathbb{R}$. The position of agent $i$ is denoted by $x_i\in \mathbb{R}$ and the location of ...
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Different payouts of pure strategies in mixed strategies
I have a question with mixed strategies.
The question is as follows, if we're in a strategy profile that is a Nash equilibrium and a player is playing a mixed strategy, can the pure strategies that ...
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Understanding mixed strategies
I would like help with the following:
Assume a game with two individuals. Suppose that for an individual a mixed strategy $\sigma_1$ is dominated by an strategy $\sigma_2, $ it is necessary for $\...
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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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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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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 ...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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?
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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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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 ...
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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 ...
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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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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 ...
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Argue that no further mixed Nash Equilibria can exists
I'm looking at the following Normal-Form Game:
...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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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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 ...
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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 ...
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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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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 ...
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