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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Game theory classic literature and specific topics

I am starting this conversation because I am searching some book in game theory for the classic problems that the literature encounnters. More precisely, I would like to know if there is some book ...
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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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1answer
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Rigorously Defining Newcomb's “Paradox”

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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1answer
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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 ...
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Trembling hand perfection and weakly dominated strategies

It is well known that players cannot use weakly dominated strategies in a trembling hand perfect equilibrium. My question, however, is a little different: does iterated deletion of weakly dominated ...
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Moral hazard, bubbles, and economies of scale in limited companies and organizations

http://eprints.lse.ac.uk/100058/1/Goodhart_CEPR_DP13494.pdf What would be the disadvantage of limiting the liability to the product of the proportion of the company and the debt(a person with 2% of a ...
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29 views

Incentive Compatibility Construction Rule

Suppose we are interested in constructing an incentive compatibility constraint for an agent to announce his state truthfully. Consider a simple case of the state space being $S=\{H,L\}$ and his ...
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Is a proft tax not distorting unless we know the opportunity cost?

A Profit tax where we actually know the Entire Cost Function Including the Opportunity cost(Time, Incommodation, best alternative for the easily monetized resources etc) is not distorting. But the ...
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Features of the set of Bayes Correlated Equilibrium in a single-agent decision problem with uncertainty

I would like your help to better understand the notion of Bayes Correlated Equilibrium (BCE) in a single-agent decision problem with uncertainty The notion of BCE is provided in this paper for a ...
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1answer
37 views

Incomplete information in multi stage game

I would like to solve a game where firms have private information about their own type, but only know the distribution of the other firm's type. They interact in two stages, where the strategies ...
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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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1answer
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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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Direct revelation mechanism's sets of strategies and types

Mas-Colell, Whinston and Green in Microeconomic Theory describe the direct revelation mechanism as it follows: The employed notation is the following: $θ_i$: Player i's type $Θ_i$: Set of types for ...
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What are ways in which world markets are zero-sum games?

Mercantilism is notorious for treating the world economy as a zero-sum game, wherein the local economy is supposed to benefit when regulations that operate to the detriment of foreign economies are in ...
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game with payoffs defined by some stochastic process

I am trying to find examples of games that follow a similar line to the following. There are 2 players and the corresponding strategy set is $S_{i} = {x_{1}, ..., x_{m}}$ for $i = 1,2$, with $m > 1$...
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Two Players Different Strategies in infinitely repeated game

I am vexed by a Game Theory question regarding infinitely repeated games. Usually, strategies such as Grim Trigger or Tit-for-Tat are discussed in a context where both players have the same strategy. ...
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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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Value Function For Durable-Good Monopolist with General Distribution

It is known that with a unit mass of consumers, each of whom has a value distributed between 0 and 1, one can think of the monopolist solving \begin{equation} \max_{p} \ p[1-F(p)] \end{equation} when ...
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Maximum-support Nash equilibria in zero-sum games

Context: I would like to know how likely a player is to pick a specific action, provided that he plays optimally and the action is optimal. Phrased like this, the question is ill-defined. But is there ...
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Airport problem

Assume that there are $m$ different types of aircrafts. For each type $l$, we know the number of movements, $n_{l}$, and the overall runway costs, $c_{l}$, associated with type $l$ aircrafts. Since we ...
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Is a combination of Political economics and Game theory possible and beneficial?

By Political economics I do not mean the "economical" advice given by some people(see the Wealth of Nations by Adam Smith) but rather the heavily mathematized subfield of Economics studying and trying ...
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How to solve for the potential of a cournot duopoly problem?

So i have this question And i have no clue on how to get to verifying that that function on the answer sheet is a potential Cournot game. I started answering the question like this, but then i got ...
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1answer
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Robust predictions in single-agent decision problem with uncertainty

I would like your help to better understand the possibility of using the notion of Bayes Correlated Equilibrium (BCE) in a single-agent decision problem with uncertainty to make predictions on optimal ...
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1answer
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Confusion about multiple information Sets

I'm confronted with the following situation: First of all nature decides which of two games is played. Then each of two players make a simultaneous move, but only player I knows which game is played....
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The notions of Bayes Correlated Equilibrium and Bayesian Nash Equilibrium in a game with one player

I would like your help to use the correct terminology to define a Bayes Correlated Equilibrium (BCE) and a Bayesian Nash Equilibrium (BNE) in a "game" with one player. The notion of BCE in an $N$-...
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1answer
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Monotonicity of second price auctions with bidder-specific reserve prices

I am having difficulty understanding the problem below: Given CDFs $F_1, ..., F_n$, prove that the allocation rule of a second-price auction with bidder-specific reserve prices is monotone. The item ...
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I cannot find for this Simple shared effort level game

Each player can contribute to the project with non-negative effort. Player 1's utility is $u_1=e_1(1+e_2-s\cdot e_1)$ where $s\in [0,1]$. Player 2's utility is $u_2=e_2(1+e_1-e_2)$ For case 1, ...
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The difference between a Nash equilibrium and Bayesian Nash equilibrium [closed]

What is the basic difference between Nash equilibrium and Bayesian equilibrium?
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What is the most general definition of “the core” in game theory?

I’ve seen definitions of “the core” that rely on some specific assumptions, such as that the game is one of a transfer of resources, or that there is “transferability of utility” (presumably intending ...
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Sequential Game is Extensive form game?

Dynamic, Sequential, Stochastic, Extensive form and Evolutionary games. I know what all of them mean very roughly. I want to clarify them. As I understand Extensive form is a description of a ...
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Subgame perfect Nash equilibrium with incomplete information [duplicate]

Take the following two-stage game with incomplete information and simultaneous actions in each state. (1) In the beginning of stage 1 players 1 and 2 do not observe the value of $\epsilon$ but they ...
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1answer
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Definition of subgame perfect Nash equilibrium

Take a two-stage game with complete information and simultaneous actions in each state: (1) Player 1 and 2 simultaneously choose action $a_1\in A_1$ and $a_2\in A_2$ respectively. (2) Player 1 and ...
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Fehr & Schmidt, ultimatum game, inequaltiy aversion, perfect subgame Nash equilibrium

I am preparing for an exam. I have found an old exam but I have no solutions for it, so I tried to solve it, but I dont know if I did it correctly and need therefore your help. The problem looks as ...
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1answer
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Convert a sequential move game into a simultaneous move game

A statement from Ponssard and Zamir "Zero-sum sequential games with incomplete information" at the bottom of the first page reads AM's result is for zero-sum two-person games in which the two ...
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NASH equilibrium [closed]

How to approach questions like these: In a two player static game with a discrete strategic space that permits each player to chose one of the four possible strategies what is the maximum number of ...
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Stay or switch game

Consider a game consisting of two players, P1 and P2, played over multiple time steps. Refer to P1 as she and P2 as he. State: Each player can be at one of two locations, A or B. Writing the possible ...
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1answer
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Clarification on the definition of Bayes Correlated Equilibrium

I would like your help to understand the definition of Bayes Correlated Equilibrium (BCE) in an incomplete information game at p.7 of this paper. Let me summarise the definition provided in the paper....
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1answer
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Stackelberg Oligopoly 3 firms [closed]

Imagine that there are 3 firms in a monopolistic market, F1, F2 and F3. Firms 1 and 2 are incumbent firms and act simultaneously whereas Firm 3 observes the actions of both firms before deciding ...
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Implications of the concepts of combination/expansion of an information structure

I would like your help to understand the concept of combination/expansion of an information structure in the incomplete information game at p.6-9 this paper. Let me summarise the game as described in ...
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Sequential game equilibrium strategy question

The question asks for player B's equilibrium strategy, hence shouldn't player B choose the strategy that gives the highest payoff after player A's move? Why does player B choose 4 over 5 and 6 over 8 ...
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Optimal pareto in two-person game

For what values $x$, $y$ the profile $(D,L)$ is Pareto optimal? \begin{array}{c|ccc} & L & R \\ \hline U & x,5 & x+2,y \\ D& 1,-1 & x,0 \\ \end{array} Is correct $x<1$ ? ...
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Condition for a Nash equilibrium

Consider two people have a mutually advantageous relationship. That is, if both dedicate more effort to the relationship both improve. Specifically, each individual chooses a level of effort $x_{i}\...