# Questions tagged [game-theory]

Game theory is a study of situations of strategic interaction between two or more players in which there is a predefined set of rules and an outcome associated with each choice taken.

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### Finding Bayesian Nash Equilibrium

I'm recently new to Game Theory and I've recently started teaching myself about Bayesian Nash Equilibirum. I've stumbled across a problem set that I can't seem to wrap my head around concerning ...
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### What is “indirect mechanism” in the context of adverse selectoin?

On this slide deck, page 12, it says "then this direct mechanism implements exactly the same allocation as the indirect mechanism we started". What is indirect mechanism in this context and in ...
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### If the players are symmetric and the core is nonempty, then $x_i = v(N)/n$ for all $i$ is a Core element

Consider a TU game $\langle N,v \rangle$ with $N = \{1,2,\ldots,n\}$ being the set of players and $v : 2^N \to \mathbb R$, $v(\emptyset) = 0$ the characteristic function. The Core of $v$ is defined by ...
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### How to write down a normal form of the game with information set?

How can we write down a normal form for this following game with information set? (The picture is modified from a picture from Wikipedia.)
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### Does the case of strategic complements always result in a situation where the Stackelberg leader is worse off?

For example, in the case of Bertrand competition, is the Stackelberg leader worse off relative to the follower? If so, why? Is this because the first mover can always undercut until marginal cost is ...
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### Renewal of multiple notions of value in contemporary (green, public good) economy and are there general game theories?

https://en.wikipedia.org/wiki/Exchange_value mentions 4 notions of value: economic value, exchange value, use value, price. But this article also mentions that these are Marxian concepts and the ...
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### Existence of symmetric trembling hand perfect equilibria

Consider symmetric and finite game. By Nash (1950), the game must have at least one symmetric equilibrium (proof). Also, it must have at least one trembling hand perfect equilibrium (proof). ...
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### Clarification of iterated prisoners dilemma

In the description of an iterated prisoner's dilemma on Wikipedia, it states that in order for a game to be considered iterable, it must conform to the rule 2R > T + S, where R is the reward for ...
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### Evolutionary stable strategies

I am new to evolutionary game theory so I can't figure out whether I'm looking at things correctly. I have the following payoff matrix: $$A = \begin{matrix} 3 & 0 \\ 5 & 1 \end{matrix}$$ ...
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### Risk neutrality in single-agent choice problem under uncertainity

Consider the following static single-agent choice problem under uncertainty. Let $V$ be the state of the world with support $\mathcal{V}$ and probability distribution $P_V\in \Delta(\mathcal{V})$. ...
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### Bayesian Correlated Equilibrium in a one player case: relation with literature

I am curious about the connection between one-player Bayesian Correlated Equilibrium (hereafter, BCE) introduced by Bergemann and Morris for a generic $n$-player setting with $n\geq 1$ (here) and the ...
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### Cournot Duopoly and Non existence of best response function

Is it possible for a cournot duopoly game to not have the best response functions? I have a profit function whose first-derivative is piece-wise. When I solve for one player's quantity (decision), it ...
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### Signaling in zero-sum games?

The foundation of this question is a bit vague (based on something overheard at a conference) but I'm hoping someone here can provide some clarification. I overheard a conversation between two ...
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### Who took utimatum game and dictator game as the evidence against Homo Economicus assumption of individual utility maximization?

Wikipedia and this McGill University page states that the two games "have been taken as both evidence for and against the Homo economicus assumptions of rational, utility-maximizing, individual ...
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### How does your dominant strategy change in a second price auction if there are two items?

Suppose there are 4 individuals and two items in this particular auction. I understand that the dominant strategy in second price auction is to bid your true value if there is a single item but I'm ...
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The classic literature refers to the problem where information asymmetry exists between an informed and an uninformed counterpart as the adverse selection problem, but how can we verify what kind of ...
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### A question about the proof of minmax theorem

I'm reading the lecture note about minmax theorem in zero-sum game. First are the relevant definitions used in my lecture notes: A finite zero-sum game, or matrix game, is given by a real-valued ...
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### Cross derivatives of payoff functions in potential games

In Monderer and Shapley (1996) (pdf) there is the following theorem. The next theorem is well-known (and very useful). THEOREM 4.5 Let $\Gamma$ be a game in which the strategy sets are ...
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### Sequential Price Competition for Perfect Complements

There are two goods, $1$ and $2$ produced by two firms at zero marginal costs. The goods are perfect complements. The demand for each goods is: $Q_1=Q_2=a-(p_1+p_2)$. The prices are set sequentially, ...
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### Bertrand Duopoly Equilibrium for Discrete Prices

There are two identical firms, $1$ and $2$, with zero marginal costs. They produce homogenous product, which is demanded by a unit mass of identical consumers, each of which has inelastic unit demand ...
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### Modeling risk aversion. Expected utility function

I want to model an Expected Utility Function for risk aversion but my problem is uncertainty in itself. I want a function(a special case) f(x, y) =\left\{\begin{matrix} h(bx^{1-C}+ay^{1-C}),C\neq 1\...
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### Framing Effect Risk-Aversion Risk-Pursuit

I am an economics' graduate seeking to study Law and I want to illustrate the importance of legal certainty. Penalties, Costs are negativelly framed. I am trying to word. 200 dollars with 50% ...
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### Unique Nash-equilibria in multi-unit auctions with uncertain participation

Setup Consider a one shot sealed bid multi-unit auction where $N$ bidders compete for $K$ identical objects and each bidder $i$ has demand $d_i\in \{1,\dots,K\}$. Bidders receive private i.i.d. ...
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### What do game theorists think of behavioural economics?

Though behavioural economics has been popularized over the past decade in both industry and pop culture, it seems that not much has changed with regard to the standard economic definition of ...
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I was surprised to find that we did not have a question on this Stack Exchange on this particular problem in decision theory. So I have chosen to add a question on Newcomb's Paradox, though I would ...
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### Is Bayes correlated equilibrium relevant for dynamic games?

Consider the following classification of solution concepts ...
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### How far must one reason up the belief hierarchy?

In games of imperfect information, one must reason about the belief on the state of nature, the beliefs of other player's beliefs of their beliefs, and so on. This is referred to as the belief ...
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### Is the set of optimal strategies convex in a single-agent decision choice problem?

EDITED with insights from the comment below. Consider a decision maker who has to choose an action among $\mathcal{Y}\equiv \{1,2,...,L\}$. The payoff from choosing action $y\in \mathcal{Y}$ depends ...