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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Auction with independent private values - An example from Game Theory: Analysis of Conflict by Roger Myerson
I have difficulties understanding the equilibrium analysis of the following auction game:
Suppose that there are $n$ bidders in an auction for a single indivisible object. Each player knows privately ...
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Can someone help me with constructing the strategic form and calculating the set of Nash equilibria in pure strategies? [closed]
I'm trying to solve it but my solution are different every time.
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Using Variance for Nash Equilibrium
For the mixed strategies, the expected utility (or payoff) is used to find the mixed strategy Nash Equilibrium. The main assumption is players try to maximize their expected payoffs. However, I think ...
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Mixed Strategy Nash Equilibrium
Consider the game of Battle of Sexes, where
$$\begin{matrix}
&&Women\\
&& Football & Resaurant\\
Men&Football&2,1 & 0,0 \\
&Restaurant&0,0 & 1,2
\end{...
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Ultimatum game where fair offers are automatically accepted
Has there been any experiments with a variant of the Ultimatum Game where a fair offer is automatically accepted?
For example, the game below, where rule 2 has been added to the classic ultimatum game:...
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Finding strategies and subgame perfect equilibria
In my game theory class we recently learned about dynamic games and I wanted to know whether I solved my homework problem correctly (and how to attempt the second part).
a) Determine all strategies ...
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Question on One Shot Deviation (Game theory)
Found this question in my practice set. This seems like a conceptually important question regarding the topic One shot deviation but I have absolutely no clue how to solve it..
Would prefer an in-...
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Equilibrium of Perturbed Dollar Auction Game - An Example from Game Theory: Analysis of Conflict by Roger Myerson
I am studying game theory using Myerson's textbook (Chapter 3 - Equilibria of Strategic-Form Games, Section 3.6 - The Decision-Analytic Approach to Games). I have difficulties understanding and ...
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Can There Be a Dominant Strategy If Both Firms Choose to Match the Lowest Price in the Market in a Bertrand Model of Competition?
In a Bertrand duopoly model where firms choose to price match ie match the lowest price in the market, any price p∈[c,Pm] (where c is cost and Pm is the monopoly price) can be a Nash. Hence, there are ...
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Nash Equillibrium - Depend On The Opponent's Strategy?
Say I have the following pay-off matrix:
For a one-shot game, it is easy to see, that (low, low) is the only Nash Equillibrium in the payoff-matrix.
However, say we're playing an infinitely repeated ...
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AIC Calculation
Our object is calculating AIC, and we are unsure whether we can use our measure below when calculating AIC. The following are the data from the experiments and our method to calculate the information ...
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Cutoff rule-mechanism question
I was checking on this paper where they define some rule-mechanism that is called cutoff rule-mechanism. I do not really understand why is this useful and how is this defined. Any help would be ...
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Stackelberg equilibrium with arbitrary number of firms
Consider a market, where N firms with average cost c compete in quantities. Assume linear demand P=a-bQ. Assume that N is arbitrary.
a)Find the equilibrium of the game, where these N firms compete a ...
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Proving the existence of mixed-strategy NE for 2-player zero-sum symmetric game
I am trying to prove the existence of mixed-strategy NE for 2-player zero-sum symmetric game, under the condition that given they have $I$ pure strategies and for the pay-off matrix $A$, $\exists x\in ...
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Determine Whether A Preference Relation Satisfies The Continuity Axiom - from Exercise 1.1 in Game Theory: Analysis of Conflict by Roger Myerson
I am self-studying game theory using Game Theory: Analysis of Conflict by Roger Myerson. Here is an exercise from the textbook. I tried it myself, but I am not sure if it is correct. I would really ...
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Principal agent problem with correlated output
I am a bit confused by one question I am working on since some of the questions seem to suggest a differnt answer from the one I get in the earlier question. Here is the exercise and my working.
One ...
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What is the relation between Blackwell's order and Stochastic Dominance order?
In Kamenica and Gentzkow (2017) as well as in Bergemann and Morris (2016) the notion of Blackwell comparioson of experiments is used to compare different information structures. I am trying to find ...
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Name for games where the i'th player's utility depends only on the actions of players 1 to i?
Consider the class of normal form games with strategy sets S_1, ..., S_n, where each player's utility function depends only on its own and the previous players' strategies. i.e. u_i(s_1,...,s_n) = u'...
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what to learn to write a comprehensive strong paper?
to write an excellent comprehensive paper, what topics and techniques must an economist learn? One of my former professors wrote a paper I read, there are theories, calculations, and empirical tests. ...
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About The Bayesian Conditional-Probability Systems in Myerson's Game Theory: Analysis of Conflict
I am self-studying game theory using Myerson's Game Theory: Analysis of Conflict. I got some trouble understanding his Bayesian conditional-probability system. The Bayesian conditional-probability ...
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General equilibrium with market power
I'm trying to solve the following problem:
Consider an exchange economy with two consumers, $A$ and $B$, whose utility functions are:
\begin{align*}
u_{A} & = x_1^A x_2^A \\
u_{B} & = x_1^B (...
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About Theorem 1.1 in Game Theory: Analysis of Conflict by Roger Myerson
I am self-studying game theory using Myerson's Game Theory: Analysis of Conflict. I got some trouble understanding his proof of Theorem 1.1, the Expected-Utility Maximization Theorem. The Theorem goes ...
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How can I show what a discount factor is a function of in a bargaining model?
I was reading Espinosa and Rhee (1989) and I was wondering how can the impact of exogenous changes on the discount factor can be shown mathematically. For example, if $A$ represents some exogenous ...
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How much information is required to manipulate a mechanism?
It is well-known that the first-price auction is manipulable, in that a player can improve his utility by bidding less than his true value. But successful manipulation requires information: the player ...
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How do I solve this exercise (My attempt is included)
Suppose that each wind turbine needs an area of one acre and produces electricity that can be sold for one money unit. Our partial market has six agents $1, \ldots, 6$. Agent $i, i=1,2,3$, has $i$ ...
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Beer-Quiche Game - Hybrid Equilibrium
Can a hybrid equilibrium for the following game be found?
Cho and Kreps (1987) introduced what is now a famous two player signaling game. First, Nature selects player 1, who knows his type, to be ...
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Trouble Understanding Dominant Strategy in the Prisoners Dilemma
Here's a payoff matrix for a Prisoners Dilemma:
Alpha is supposed to be the dominant strategy, which means that "no matter what my pair chooses, I will be better off playing Alpha than playing ...
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Signalling Game - Extensive Form
I am drawing the extensive form for Beer or Quiche game. Is there any difference in the following two representations or can either one can be used for representing the same information?
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Can von Neumann Morgenstern utility be negative?
I saw this question in stackexchange that a utility function can take negative values.
I did not read any thing from the axioms that utility cannot be negative. It states they must be in the set of ...
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Monopoly Board Game Situation Modeled With Game Theory
Three players are playing the board game Monopoly. All properties are acquired, and only Player A has completed a color group. This also leaves Player A with very little cash. Player B and Player C ...
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Signaling game (beer and quiche) and consistent beliefs
I am confused why the top left node has numerator (9/10x1/9) instead of (1/10x1/9) since this should be the probability of reaching this node given the strategies? Same with upper right node, why is ...
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What is the difference between utility, payoff and expected utility, or are the terms interchangeable?
I've started teaching myself game theory recently, but so far I haven't come across anything clarifying these terms .
This is my understanding of the terms based on what I know:
Payoff = Utility. ...
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Optimality of the free market and game-theoretic arguments
I recently heard an informal argument that went something like this:
Through individual self-interest and freedom of production and consumption, the best interest of society, as a whole, are ...
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Finding Subgame-Perfect Nash Equilibrium in Games of Imperfect Information
How to proceed in the following finite game of imperfect information to solve for subgame perfect Nash equilibrium? The only subgame is the game itself. And by converting the extensive form into a ...
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Definition of information structure in an incomplete information game
I try to understand the model in this paper, pages 48-49. (Bergemann, D., & Morris, S. (2019). Information design: A unified perspective. Journal of Economic Literature, 57(1), 44–95. https://doi....
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Looking up actions dominated by mixed strategies. Any mixture or only uniform?
In all examples I saw describing the Iterative removal of strictly dominated strategies, the case of actions removed because dominated by a mixed strategy of the other actions where always given with ...
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Nash equilibrium in p-beauty contest game where p=1
Setup: players must chose a number between 0 and 100. The winner of the game is the player whose chosen number is closest to the average of all chosen numbers multiplied by "p". Assume that ...
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question about lemma 1 of Crawford & Sobel (1982)
In Crawford & Sobel (1982), they proved in lemma 1 that for the basic model of a cheap talk game, every equilibrium induces finitely many actions. Here is a special case of their model where the ...
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Profit Maximizing with a competitive fringe
I have this question:
Your business is the dominant firm but there exists a competitive fringe.
The competitive fringe produces with total cost: $\; c_𝑓(q_f) = 3𝑞_f$.
There have also been some ...
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Extensive Form of Games
Is there any reason for the differing shapes of game trees when we use extensive form representation? For instance, why does the job market signalling game and the repeated Prisoner's Dilemma take the ...
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Expected number of players buying a product
There is a continuum of players who want to buy a product. The utility to each player from that product is $q$. If he does not buy the product, his utility is zero. The random variable, $q$, has a ...
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Proving existence of a unique pure strategy Nash Equilibrium in two-person continuous games
I am working on a game theory exercise and I want to prove existence and uniqueness of pure strategy NE for a 2 person game with continuous strategy spaces. Lets call the payoff functions $\pi_1$ and $...
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First price sealed-bid auction with discrete bids
I really couldn't solve this problem. Can someone help me with this?
Consider the sealed-bid auction for a single item, where there are only two
allowable bids. There are two risk-neutral bidders who ...
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Two questions in Bergemann and Morris (2016) - BCE and Comparison of Information Structures in games
Based on Begemann and Morris (2016) we have the following definition about a standard game of incomplete information
A standard game $\Gamma = <G,S>$ of incomplete information consists of a set ...
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Game With Natural Disruptions
Consider a static game with complete information, where each player makes a decision $a_i$ and receives a payoff $\pi_i(a_i,a_{-i})$.
Now suppose there is a natural disaster modeled by a binary random ...
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What is the difference between the utility with the ex-post or the ex-ante utility function?
What is the difference of the ex-post utility function of the utility function. For example in Bergemann and Morris (2019) the utility function is defined as an ex-post utility function. Check in page ...
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Is there a 2*2 game with a unique NE but not dominance solvable?
Is there a 2*2 game with a unique NE but not dominance solvable? If so, could you give an example of the payoff matrix?
Here is the definition of dominance solvable, "if by iterated elimination ...
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Mechanism Design with Quantal Best Response
I was wondering if there is a sensible definition of mechanism design (incentive compatibility and individual rationality) when the agent (bidder) is only boundedly rational. In the classical ...
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Number of Subgames in Asymmetric Signaling Game
In a two player, two signal asymmetric information signaling game, how many subgames are there? The sender moves first, the receiver does not see the sender type, but responds to the observed signal ...
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Total Number of Subgames in a Standard Prisoner's Dilemma
In the most basic form of a prisoner's dilemma game [2x2; Cooperate or Defect, imperfect information], how many total subgames are present?
Preparing for an exam and this solution is not available. My ...
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