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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Mixed strategy in extensive form games with complete and perfect information

I saw the lemma: "In extensive form games with complete and perfect information, any mixed strategy for player i will result in a lower or equal utility for player i compared to some pure ...
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Contradicting the von Neumann–Morgenstern axioms

This is a story taken from Shmuel Zamir - Game theory "This is a true event that occurred during the Second World War on the Pacific front,5 seems to contradict utility theory. A United States ...
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Example of games according to specific requirements

According to the following requirements (Source: Playing for Real by Ken Binmore): The game is presented to the subjects in a user-friendly way that makes it easy for them to understand what is going ...
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Level-0 in Level-k model

According to the level-k theory: ...
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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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Can a dominance solvable game have a mixed strategy equilibrium?

Prelude: we get this question about specific finite games. Let us answer it generally. (examples 1, 2) Suppose there is a two-player finite game (a "matrix game") where both players ...
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Extensive form game with multiple players

I am wondering on how to draw the extensive form with multiple players. Below is an example of the trust game. How would that look if there were two receivers with potentially different payoffs? Note ...
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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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Can a dominance solvable game have mixed strategies?

I was told that there is at least one mixed strategy for the following game, which is dominance solvable and has a pure strategy NE in DA I thought dominated strategies will never be played, so how ...
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One shot deviation principle in games with many players

This question is motivated by an example in Section 4.7.3. Open-Loop and Closed-Loop Equilibria in Games with many players in Game Theory by Fudenberg and Tirole. The definitions of closed-loop and ...
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Nash equilibrium with mutually exclusive actions

consider a zero-sum game where action space for both players are the same. I want to compute the equilibrium under the constraint that players do not use the same action. For example, if player 1's ...
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Average Discounted Payoffs in Continuous Time

While reading some theory papers that model a continuous time problem, I have noticed the way they represent the expression for average discounted payoff is of this form, where $r> 0 $ is the ...
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Do economics (as a science) provide any hints on how games with none/multiple NEs will be played in real life?

Let's consider a simple non-cooperative one period game. Let's note that it is relatively easy to run an experiment which will very closely reproduce the theoretical model (e.g. unfamiliar people are ...
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Recommended readings on the determination of bargaining power

An example of a Nash bargain can be found in how the total surplus of employment is shared between the employer and the worker (wage bargaining). Assuming the share of total surplus to be gained by ...
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Resolve Hold-Up Problems in Joint Investment

Say two agents jointly invest with a return function $f(i_1, i_2)$, which is increasing in both and concave, and they share the return by ratio $\beta_1$ and $1-\beta_1$. Then the result of investment ...
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Coordination BNE

I don't have a lot of experience on BNE so this question got me stumped. Two player simultaneously have to decide whether to go to a movie, i.e. to Show up (S) or not (N). They prefer to go together, ...
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Intuition of solution concepts in Non-cooperative games

I am now reading Nash's 1951 paper Non-cooperative games and I am trying to understand the intuition behind solution concepts. Solutions(Nash 1951) A game is solvable if its set $S$ of equilibrium ...
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Symmetry of a game

I am now reading Nash's 1951 paper Non-cooperative games and I have a question about the definition of symmetry of a game. Symmetries of Games(Nash 1951) If two strategies belong to a single player ...
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Nash Equilibrium with Constraints on Decision Variables

I am trying to solve a two player game with constraints on decision variables. The general structure looks something like this: $$\max_{x_1} f(x_1, x_2)$$ $$\max_{x_2} g(x_1, x_2)$$ subject to $$x_1 + ...
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Majority Voting Game

There are three players with three alternatives A,B, and C. Players simultaneously vote and majority wins. If no majority then A wins. Payoffs are: $U_1(A) = U_2(B) = U_3(C) = 2$ $U_1(B) = U_2(C) = ...
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Proof of a lemma about PPE

Dear all, I am studying the repeated game with imperfect monitoring. I have so many questions about the proof of lemma 3.6 in slide 22. First of all, why we can write $$ P_{\widehat{\sigma}_{i}, \...
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Setting up the model for a pie-sharing problem

I am buying an item (which I value at, say, a million dollars) for \$$100$. My friend has a special offer that expires today, and which he can never use again unless used by me, which gets me the item ...
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Does Cournot competition have unique Nash Equilibriium in more than 2 firms?

My approach for two cases was to draw reaction functions and successively eliminate what could not be played using rationality and common knowledge of rationality. I found indeed there is a unique NE ...
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Public/private knowledge in auctions

Consider three firms that engage in a first-price auction. Firm $i$'s payoff when firm $j$ wins the auction is $S_{i,j}$, which is deterministic and publicly known. The winning firm $i$ has to pay ...
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When is the set of rationalizable strategies a proper subset of the set that survives IEDS?

When is the set of rationalizable strategies smaller than the set of strategies surviving Iterated removal of strictly dominated strategies. Mas Collel Page 243, claims set of rationalizable ...
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Looking for a paper on game theory as a beautiful thing, not needing immediate purpose

I am looking for a paper I am sure to have read a while ago, but cannot recall its title. The message was that we should not judge game theory (or economic theory in general?) by its ability as an &...
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(Game Theory) Why is voting for your worst alternative a weakly dominated action?

I don't fully understand why voting for your worst alternative is a weakly dominated action. The question comes from a question I'm working on: "Assume there are three candidates, A,B and C,...
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How do we have no–envy for the Final Target Score here in assessing the consequences of individual changes on game dynamics and appeal?

Assume that a new Chess-variant designed to increase the level of competition throughout the game, provide additional excitement at the finish: "A Final Target Point will be set." The Final ...
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Multiple equilibria for zero sum game?

Is there any example of a zero-sum game with multiple equilibria?
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2 votes
1 answer
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Convex Preference in Nash Equilibrium

Arrow Debreu (AD) uses the convex preference (A4 among their four assumptions, also see the assumption IIIc in AD 1954 ECTA) to make general equilibrium (GE) exist, unique, and well-behave. What ...
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Best response to convex combination of strategies

Suppose that several pure strategies in a 2-individual game have pure strategy best responses. Can we say that best responses to convex combination of those pure strategies still lie in the convex ...
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Meaning of 'general case'

I was working on this problem (part a) and I was wondering what is meant by the term 'the general case'. Does this mean just make assumptions c>0 and v>0 then just solve? or should i approach it ...
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Two-dimensional hotelling equilibria

Customers are heterogeneous with regard to their preference for quality $q$. Specifically, a customer's utility from buying a product of quality $q$ at price $p$ is $V-p + \lambda q$, with $\lambda$ ...
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Is the mixed strategy $\sigma_i^*:S_i\times\Theta\to\Delta(A_i)$ chosen by player $i$ linear?

Suppose that we have a Bayesian game, where the number of players is $I$ and we refer to the generic player with $i$ $\Theta$ stands for the state of the world, where $\theta\in\Theta$ is the typical ...
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4 votes
2 answers
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Any good resources on Information Economics Theory?

I am coming from a political economy/public choice perspective, trying to explore some ideas in signaling, especially the supply-side analysis of information transmission by the media/news. Although I ...
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I present a communication game - Could you please make comments on my assumptions, notation and properties that I may have not considered yet?

I consider the following communication game. Suppose that we have $I$ players and each one of them learns a private signal $s_i=(s_{i,1},s_{i,2},...,s_{i,k})$, where $k$ is finite and also, every ...
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1 vote
1 answer
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Do there exist matrix games with more than two players? Can we extend existent models that have already used in signaling games?

In game theory, the simplest way to represent a two player games is with the help of matrix games. For example, assume that we want to model a market of traders, where one is a speculator and the rest ...
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Distinguishing Between Different Terms in Economics

I have no background and Economics and am trying to teach myself about some basic things in Economics. For example, I am trying to understand the following terms: Nash Equilibrium Optimal Strategy ...
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1 answer
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Game for negotiations

For a while I've been bouncing around an idea for a game to be used in negotiations, with a quantitative voting element. The basic idea goes like this: there is a list of things each side of the ...
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Pareto optimal solutions

Suppose $U_1(x,y) = y - 0.5x$ and $U_2(x,y) = x - 0.5y$ where $U_i$ is the pay-off function of player $P_i$. What are all the pareto optimal solutions for $x,y \in [0,1]$? I can't think of a way to do ...
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Is there a term of a "basic" Game Theory Game?

I am trying to learn more about Game Theory - here is a game I invented: There are two Players: Player 1 and Player 2 There are two Coins: Coin 1 and Coin 2 Coin 1 lands on "Heads" with a ...
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2 votes
1 answer
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A question about revelation principle from the game theory online course

I am finding the revelation principle very confusing. So I was watching the Game Theory online course by Stanford and UBC. In their video about revelation principle, here are the original words from ...
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Creating a Game Theory "Game"

I am trying to create a simple Game Theory game in which : Two players are competing against each other (Player 1 and Player 2) Each player can either perform "Action A" or "Action B&...
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1 answer
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Revenue-maximizing auction with no free disposal

Myerson has a famous theory that can be used to design truthful auctions maximizing the revenue of the seller. The simplest case is when a seller sells a single item to buyers whose values are ...
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2 answers
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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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1 vote
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bargaining game information/equlibria/gametree/normalform

I have a game with two players, player one offers player two one of two cars, car 1(M) has value 2 and car 2 (H) has value 1. Player two can accept (A) or reject (R) the offer. Now I have to answer ...
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Bayes Nash equilibrium distribution

I would like to define a decision rule that is induced by a BNE distribution in a game with a continuum of agents. For that, I have a decision rule $\varphi:\Theta \rightarrow\Delta(\Delta(A))$ that ...
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1 answer
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Game Theory Model needed to model the question whether "not taking the covid vaccine is free-riding"

I am a student and completely new to Game Theory, in fact, it is an additional course for me, I am actually from an entirely different field. I am asked to choose a Game Theory approach to model the ...
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How to define a majority function in a communication game?

Suppose that we have a communication game of $N$ players. Every player $i$ receives a tuple of $N-1$ messages that is a recommended strategy of the other player $j$. I define the recommended ...
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3 votes
1 answer
241 views

Conditional Expectation of state after observing public and private signals

I am reading Social Value of Public Information by Morris and Shin(2002) and I have a question about calculating the conditional expectation after observing both public and private signals. In their ...
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