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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Confusing Bertrand Problem [closed]

I am attempting to solve a Bertrand Equilibrium. I am given the information: $$p_1 = a-q_1-bq_2 \text{ and } p_2=a-q_2-bq_1$$ Profit = $(p_1-c)q_1$ for firm 1 and the same thing respectively ...
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$a\geq 0$, $x\succsim y$ implies $x+a\succsim y+a$ so the preference is linear?

$\succsim$ is a continuous and local non-satiate weak order. $x,y,a$ are vectors in $\mathbb R^n$ We say $a\geq0$ if all directions of the vector $a$ is greater or equal to zero. We want to prove (...
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1answer
41 views

Difference(s) between Rational Expectations Equilibrium and Nash equilibium

What is the major difference between the notion of rational expectations equilibrium and Nash equilibium? And why do we, only, have a rational expectation about the first moment (the price) in the ...
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Game Theory - Trying to find a 2x2 game that represents this interval [closed]

I know how to calculate equilibrium, however, how do I work backwards? i.e. How do I find the payoffs that correspond to a set of mixed Nash equilibria whereby the interval for Player 1 is exactly ...
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I'm having a hard time solving this game to see if pooling can be sustained [closed]

The problem states: "Consider the extensive form game of kitchen work below. Can a pooling equilibrium be sustained? Show mathematically and explain intuitively.
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Showing that some outcome of a repeated game is a subgame perfect equilibrium

We have a twice-repeated game with its stage shown by the payoff matrix below. $$\begin{array}{c|c|c|c} & \text{L} & \text{C} & \text{R}\\ \hline \text{T} & (1, 1) & (5, 0) &...
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1answer
60 views

$a\geq 0$, $x\sim y$ implies $x+a\sim y+a$ so the preference is linear?

$\succsim$ is a countinuous and convex weak order. $x,y,a$ are vectors in $\mathbb R^n$ We say $a\geq0$ if all directions of the vector $a$ is greater or equal to zero. We want to prove (or ...
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1answer
37 views

$x\sim y$ implies $x+a\sim y+a$ for any $a\geq0$ and $x,y\in\mathbb R^n$, then the preference is linear?

$x,y,a$ are vectors in $\mathbb R^n$ We say $a\geq0$ if all directions of the vector $a$ is greater or equal to zero. We want to prove (or disprove by counterexample) that: Suppose $x\sim y$ ...
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1answer
32 views

Example of information structure in a one-player Bayes Correlated Equilibrium

Model Consider a game where a decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world. The state of the world has support $\mathcal{...
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5answers
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How to analyze this guessing game?

I sometimes play a guessing game with a friend. So fx we might try to guess how many people live in Russia. So person A says 100 milion and then person B says either 'more' or 'less'. If B says 'more' ...
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1answer
28 views

Uniqueness of equilibria in first-price auction with discrete valuations

Assume we have a first-price auction with discrete and independent private values and identical distributions of all bidders. It is known that there exists a Bayes-Nash equilibrium where bidders bid ...
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1answer
21 views

SPNE in two matrix

Is it correct that I have underlined in this matrixes? And therefore the correct answer is (A) ? Or should I do this like a tree game rollback like this: And with the roll back scenario we play like ...
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1answer
92 views

Is the Nash product really maximised ex post?

In my game theory class this term, we studied Nash bargaining. It is only now when starting to prepare for the exam that I have come to realise there is something I fundamentally don't understand, and ...
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Analytically solvable examples of quantal response equilibrium

I have been reading up on quantal response equilibrium and am looking for some simple examples which can be solved analytically (in order to gain some intuition about how exactly QRE works). To be ...
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1answer
43 views

Grim strategy and SPNE

I know how to play the Grim strategy for player 1 for example we go: $$40 + \frac{25}{R} > x + \frac{1}{R}$$ And solve for $R$ (= rate) But I'm not quite sure what my $x$ should be. Or in ...
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SPNE with 3 players in a three

First picture: we always do the roll back scenario, (B,M,F) so Francisco start and 2 > 0 in the last node so therefore he will be in. And if Franscisco is in, McDonalds at the last node, have to ...
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1answer
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Limited Liability in Agency Problem

Consider a simple one-period model where a creditor provides $I$ as investment to a firm and firm produces $\pi_G$ or $\pi_B$ depending on its performance. Let $R_i$ the portion of the profit that the ...
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1answer
21 views

Computation of Different Axiomatic Barganing Solutions

I need help with the following question. Take a two-agent bargaining problem. d=(0,0). Pick a strictly concave function for the bargaining frontier. Fix the intersection of the frontier with the y-...
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51 views

Game theory: SPNE and simultaneous move games, Interpret it in a tree [duplicate]

Question: And the solution: It says in the question, that Franco can eat half or almost all. And after that, Francisco can choose to give the whole roll to the ducks or eat the rest of it. I don'...
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2answers
50 views

Extensive Form Representation

Question: Represent the extensive form of the game: Suppose, Nature chooses either Up or Down with probabilities 0.5 and 0.5, respectively. Then Player 1 chooses either Right or Left and does not ...
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Form of recursive formula for stochastic games of one-sided incomplete information

I'm trying to understand Proposition 1 on page 377 of this paper. The author studies zero-sum stochastic games with one-sided incomplete information: player 1 is informed of some true state $s\in S$ ...
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2answers
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Why do game theorists use a discounted payoff of this form?

Excuse the click-baity title. I notice the discounted payoff in the game theory literature usually takes the form $$\sum_{t=1}^\infty\lambda(1-\lambda)^{t-1}R_t$$ This differs from the discounted ...
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What are examples for the phenomenon that more (or better) information makes everybody worse off?

More information is usually considered "better". Let's say a rational agent chooses optimally given his information on the circumstances of a particular decision problem. Then providing him with more ...
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1answer
41 views

Bayes Correlated Equilibrium with complete information

Model Consider a game where a decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world. The state of the world has support $\mathcal{...
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1answer
37 views

Some basic questions on infromation asymmetry

How does asymmetric information and bid-ask spread are connected? For instance, economic theory tells us that, the more the problem of information asymmetry, the higher the spread is. What is the ...
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1answer
85 views

Set of Bayes Correlated Equilibria when complete information is not available

Model Consider a game where a decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world. The state of the world has support $\mathcal{...
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2answers
55 views

Finding Mixed Nash Equilibria in a $3\times 3$ Game

I am tasked with finding all of the Nash Equilibria (pure or mixed) in the of the following game: $$\begin{array} \\&L&C&R\\ T&2,2&2,3&1,2\\ M&0,3&3,2&1,1\\ B&...
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2answers
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Information and search

Consider a game where a decision maker (DM) has to choose action $l\in \mathcal{Y}$ possibly without being fully aware of the state of the world $V$. The choice set $\mathcal{Y}$ has cardinality $L$....
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1answer
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Minimizing consumption in a single market( Partial Equilibrium)

Let there be a good X where the optimal consumption is 0; i.e the social costs for any unit provided would always be greater than the utility surplus of the market. We know that prohibiting it( ...
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1answer
59 views

Simple hawk-dove type super-game

We have the following super-game: \begin{array}{cc} & a_1 & a_2 \\ a_1 & 0,0 & -1,1 \\ a_2 & 1,-1 & -2,-2 \end{array} I want to show that both the trigger (or grim) ...
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1answer
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Refinements in signaling games with three sender types

What are the pros and cons of the Intuitive Criterion and the Criterion of Divinity in signaling games with three types? I find that separating equilibria often survive the intuitive criterion, ...
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1answer
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Is there any overlap between evolutionary and behavioral game theory

Evolutionary and Behavioral game theory are two different techniques. Both seem to be inspired from biology. So is there any overlap between their theory? Are the two complementary to each other in ...
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1answer
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Obvious Dominance and Milipede Games (Question to Pycia and Troyan (2019)

I stumbled over Millipede Games and obvious Dominance in the paper "A Theory of Simplicity in Games and Mechanism Design" by Pycia and Troyan. On page 12 the authors define millipede Games. They ...
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1answer
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What would be the consequences of Downsizing on the economy?

In the 2017 movie Downsizing, a chunk of the population decides to reduce their body size to just a few inches. What would be the consequences of this on the economy? I'd like to know chronologically ...
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1answer
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Existence of a subgame perfect Nash-equilibrium

Existence of a subgame perfect Nash-equilibrium Given is the following game The game is repeated finitely many times and the total payoff is the sum of the payoff from each repetition. If we assume ...
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1answer
36 views

Pure and Mixed Nash Equilibrium algorithm gives different results

I have a game represented by following table: It is clear that there is a pure Nash equilibrium at 4,2 (both players do not cooperate, player 1 awarded 4 points and player 2 awarded 2 points). Now ...
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1answer
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Allocating chores using auctions

I live in a student dorm with 16 people and we share a kitchen. Every week someone has to clean the kitchen. Right now we just take turns in a way determined by the numbers of our respective rooms. ...
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1answer
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Extended game mixed SPNE

I have doubts about whether my solution is right. Let $x>z>y>1$. Given the extended game above, we have two subgames and will find the Nash equilibria of these. Observe that player 2 will ...
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Behavioral Dictator Game

I am doing a self study on behavioral economics and I am trying to solve behavioral version of the dictator game with following utilities for person 1 and 2. $$ u_1( \sigma_1, \sigma_2 ) = \...
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1answer
53 views

What is the subgame perfect pricing policy for seller?

Suppose there is a seller S who is selling to 3 different potential customers H, M, L The good is a durable good and it's utility in terms of dollar equivalent is as in the picture below: So if H ...
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2answers
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Why is infinite recursion on the common knowledge assumption necessary?

If something is common knowledge in a game, that means that every player knows it, and every player knows that every player knows it, and so on. Are there cases where only one such level of knowing ...
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Market mechanism design and decision rule based on a graph

I am doing a micro course right now. I came upon this question while studying and I was hoping for help/hints on how to solve it or what resources to consult to better understand the topic. the ...
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1answer
26 views

What happens to consumer surplus and profits as firms get more information in Hotelling's duopoly model?

In the Duopoly on the line [0,1] with customers uniformly distributed, with firm A on the 0 side and firm B on 1's side, we know that if the firms have no information about the customer, there will be ...
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1answer
54 views

How to find mixed optimal strategies in this zero-sum game?

I'm trying to solve this problem from last year final exam in game theory: Consider the zero-sum game $G=(X, Y, g)$ where $X=Y=[0,1]$, and $$\forall (x,y) \in X \times Y: g(x, y)=\max \{x(1-2 y), y(...
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Who is the first person/paper to introduce “mixed strategy”?

Who is the first person/paper to introduce "mixed strategy"? The PNAS by Nash used this notion without citing anyone. Does the earlier book: Von Neumann, J., and Morgenstern, O., The Theory of Games ...
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1answer
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Is there some definition about risk sharing?

I was searching for a definition of risk sharing and I have found the following: $\underline{Definition:}$ Risk Sharing — also known as "risk distribution," risk sharing means that the premiums and ...
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2answers
37 views

What is the implicaiton of agent risk neutrality in moral hazard?

I heard that risk-neutrality of agent in moral hazard imply that the action associated with first-best and the one associated with second-best will be the same. Is it true and why is it so? Are there ...
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1answer
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What does “steep incentive contract” mean in the context of adverse selection?

This term was mentioned in a slide and when I looked online, the only thing which I could find talking about this is this paper. For example,in the cost-plus-incentive contract $$x(T, c) = a(T) - a'...
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1answer
86 views

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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1answer
23 views

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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