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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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Textbooks addressing MDP's in microeconomics/game theory/decision theory?

I have learned about the MDP formalism in the context of machine learning. I know that micro theorists also study MDP's, and agent behaviour in this context (both single and multi-agent I think). I ...
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28 views

Rigorous solution of Stackelberg leader-follower game with N-players?

In the classical two-player Stackelberg game (sequential Cournot) we have a linear demand function $P = 1 - Q$ where $Q = \sum_0^2 q_i $, and we assume homogenous production cost $c$. By starting from ...
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1answer
43 views

reference request: models of how racism or sexism affects decision making

My background is more in statistics and applied math, so I am not familiar with the breadth of decision making models from economics. However, I am working on a project that involves decision making ...
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1answer
85 views

Are direct mechanisms always truthful?

I am very new to mechanism design so I am a bit lost among the concepts, even the most basic ones. One thing that is not clear to me is the concept of direct mechanism and its relationship with the ...
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Game Theory - set of undominated action profiles

In game theory, when we talk about iterated dominance, why is the set of undominated action profiles not monotone?
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proof verification in George J. Mailath and Andrew Postlewaite (2001b)

I am reading George J. Mailath and Andrew Postlewaite (2001), and this is the lemma 1 in this paper. I don't understand the induction process in this proof. I think that we should use the fact that $...
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1answer
45 views

Perfect Bayesian Equilibria

What are the perfect Bayesian equilibria in the following game? The part that is confusing me is the right-hand side, where player 2 is of type N. Thanks! EDIT: My workings out so far are given ...
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1answer
31 views

Approximating common knowledge with common beliefs (Monderer and Samet, 1989)

I'm trying to understand Monderer and Samet's 1989 paper on approximate common knowledge. I'm stuck in the last part of the proof of the "agreeing to disagree" Theorem A, where the upper bound of the ...
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1answer
18 views

What is the monotone hazard rate assumption used for?

I was reading this article on advance purchase discounts and pricing in which the author uses the monotone hazard rate assumption. Why does the author use it? The article is Advance-purchase ...
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Find a subgame perfect equilibrium and a Nash equilibrium

I want to know if my thinking is correct. Look at the following game. As the game has only one subgame (i.e., the game itself) then the Nash Equilibria will coincide with the subgame perfect ...
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14 views

Three stage two player signalling game, pooling equilbrium

I am solving a three-stage game in which first the sender sends the signal, then the receiver acts based on the signal and finally, the sender moves again. The sender has two types high and low and ...
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1answer
30 views

How do I solve this Game Theory Bargaining problem? [closed]

Let's say there are two players in a game. In the first period, P1 makes an offer to split 3 dollars with P2. P2 accepts or rejects the offer. If P2 accepts, they get the offer made by P1, and P1 gets ...
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1answer
60 views

Cournot duopoly with differing costs

There are two firms in a Cournot duopoly that face inverse demand $P = \alpha - Q$, but one firm has total costs $c_1*q_1$ and the other has total costs $c_2*q_2$ with $c_1 < c_2$. I want to show ...
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31 views

Sender-Receiver games vs Signalling games

Is there actually any difference between Sender-Receiver games and Signaling games? Or these are two different names for exactly the same class of games?
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1answer
196 views

All-Pay Auction Mixed Strategy Equilibrium

I am currently struggling with this exercise. Professor Nash announces that he will auction off a 20 dollars bill in a competition between two students chosen at random. Each student is to privately ...
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1answer
49 views

Proving the existence of Nash Equilibrium using alternate approaches

Most of the standard books/papers/reading materials prove/state the existence of a Nash Equilibrium by appealing to Sperner's Lemma, or to Brouwer's/Kakutani's FPT. However, I've recently come to know ...
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2answers
63 views

Is there a game that cannot be represented by a game tree?

Is there a finite game that cannot be represented by an extensive form or a game tree? I know that many games are too long and complex to be represented by a tree of a reasonable size, but that's not ...
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Mean Field/Differential Game and Measurability

Consider the following scenario. There is a continuum of players in a population, with population measure normalized to $1$. Each player has a type $\theta \in [0,1]$ and we suppose that $\theta$ is ...
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1answer
78 views

Help needed to understand proof in Myerson and Satterthwaite (1983)

The following image is an excerpt taken from Myerson and Satterthwaite's 1983 paper Efficient Mechanisms for Bilateral Trading: I know what the theorem is all about, all I need is some help with the ...
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1answer
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Game Theory; Finding the Nash Equilibria

How to proceed with such problems where there is no pure Nash Equilibrium? Even if we attempt to eliminate strictly dominated strategies, we find none.
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3answers
190 views

Why are second price auctions preferred if they don't maximize expected revenue?

The reasoning usually given for why you would use a second price auction (SPA) as opposed to a first price auction (FPA) is that FPA encourage underbidding while SPA encourage truthful bidding. That ...
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Are there any experiments about financial games with just one player?

I was wondering if there are any experiments of financial games (laboratory games under controlled circumstances like Plott and Sunder's Rational Expectations and the Aggregation of Diverse ...
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1answer
33 views

General Results on First or Second Mover Advantage?

I am just wondering whether the following question has already been answered in game theory: Fix an arbitrary (say, finite) two-player strategic form game. Under what condition, does one player (say, ...
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1answer
34 views

Is it possible to have transferable utility in non-cooperative games?

Transferable utility is a concept that seems to be associated with cooperative game theory and coalitions. I would like to know if there are any examples of transferable utility in non-cooperative ...
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28 views

Query regarding best response curves

Hal Varian intermediate microeconomics ch-29(game application), page-546 to 550, subheading-games of competition. 1) in page 548, to quote the author "what about column? We can perform a similar ...
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2answers
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Straffin, P. D. (1993): Game Theory and Strategy. How is the security level on p. 103 calculated?

Could somebody explain how Straffin calculated the security levels for Rose and Colin on p. 103? As far as I understood, Colin's security level is 6 because it is the minimum of the strategy Colin A ...
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Insurance question: need a brief explanation

Two risk averse people are identical in every way (including wealth, W , amount of loss, L, and utility function, U(W)) except they have different probabilities of loss. Suppose they want to buy ...
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1answer
51 views

First Price Auction with Reserve Price

I'm trying to solve the following question: "The seller wants to auction off a single item to two bidders, the valuation of each bidder is an iid draw from a uniform distribution on $[0,1]$ where ...
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62 views

Signaling questions (separating equilibrium)

Consider two firms Inverse functions: $p(q)=max\{a-q,0\} $ $q$ is total production and a is positive constant. This value of a takes two values ah=2 (high demand) and aL=1 (low demand). Their ...
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1answer
34 views

Why is every action considered to be in the support while calculating mixed strategy equilibrium?

While evaluating the mixed strategy equilibrium, in most of the cases, we consider that all actions of a player are in the support of the equilibrium.Is it always so? I was going through a problem (...
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1answer
64 views

Market Power in microeconomic theory

What does the term Market Power mean in microeconomic theory
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1answer
98 views

Discount function

Company A needs to provide service $p$ to company B. However if the company B will reserve the $(1-\alpha)$ fraction of resource for the serving customers of company A, company A will provide a ...
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3answers
58 views

Is choosing an investment by a bank only due to its regulatory capital charge a form of moral hazard?

The main shortcoming of the first Basel Accord (Basel I) was that its capital requirements did not reflect the actual risk of the bank assets. One way this nonsense influenced the asset choice of ...
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Perfect Bayesian vs sequential equilibrium

when do we use the concept of the Sequential Equilibrium and when do we use the concept of perfect Bayesian Equilibrium to solve a problem? (for example when we have a game tree like the one in the ...
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Two-sided market and bargaining game

I am solving a bargaining problem in which I have two players $player_1 $ and $ player_2 $. Both of them have a service (represented as $ z_1 ,z_2 $) that they can provide . Moreover they will ...
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1answer
152 views

Stackelberg setup

I am completely confused because I cannot find the leader's best response. I do not know if it is exactly the same as it was a Cournot game. What I did is: Any help will be appreciated a lot. Thank ...
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1answer
207 views

Bertrand game - Nash equilibrium

The quantity is limited to 300 but the monopoly quantity is equal to 400 and gives a monopoly price of 600. But if we plug the quantity of 300 into the demand function we get a price of 700.But I am ...
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1answer
108 views

Subgame perfect equilibrium and expected profit

I am so confused because I cannot set up the monopolist's profit maximization problem.What I did is the following one: Any help will be appreciated. Thank you.
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202 views

How can I determine if a token economic is viable?

Given a system where you incentivize people to do actions in a system, we might have good and bad actors. I would like to know if there is a software or framework where I could put the different <...
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1answer
60 views

Location game between 3 firms

I could solve Question 25 (simultaneous location game between 2 firms), but I'm confused between options b) and d) for Question 26 (sequential game involving a third firm). I have attached both ...
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1answer
217 views

Finding the optimal tax

I have a problem regarding the last two questions of this exercises because I can not understand how to set up my model in order to find the optimal tax the optimal quantity to be as there was not a ...
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61 views

How to find sequential equilibria and weak perfect bayesian equilibria quickly?

I have read several texts on the nature of sequential equilibria and weak perfect bayesian equilibria (called such by Mas-Colell, also called weak sequential equilibria). I am not looking for ...
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1answer
222 views

How are ties broken in a second price sealed bid auction?

Say there are two people who evaluate an object at 5 dollars and a third who evaluates it at 4 dollars playing a second price sealed bid auction. The first two bid 5 dollars and the third bids 4 ...
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2answers
251 views

Subgame Perfect Nash equilibrium: two stage game

Charitable organizations are ranked according to the proportion of their total budget that is spend on programs(what directly goes to the recipients of their services) relative to money spent on ...
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1answer
863 views

Cournot Competition game with 3 Firms

Three firms are in Cournot competition. The inverse demand curve is denoted p(q) where p is the price if a total of q units are produced. Assumptions are: p(0)>0 and p'(q)<0 and p''(q) $\le 0$ ...
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26 views

Equivalent Texts to Tirole's Game Theory

What are some books that are on par with Tirole and Fudenberg's Game Theory, excluding Myerson, Camerer, and Sinervo & Friedman? Obviously, all these books take a different perspective on game ...
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1answer
38 views

Repeated game with stage game has more than 1 NE

Given the game like Prisoner's dilemma (infinitely undiscounted) and each person has 3 actions in every period: confess defect and kill, and the payoff matrix have 2 NE as (D,D),(K,K). Can I still ...
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1answer
713 views

3 Firm Stackelberg's Oligopoly Game

Consider a market in which there are three firms, all producing the same good. Firm i's cost of producing qi units of the good is Ci(qi)=0 for qi≥0 for each i∈{1,2,3}; the price at which output is ...
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2answers
211 views

Finding subgame perfect equilibrium

The main part of the question is as follows (if you cannot read this, I can immediately write it) My question is how to find the subgame perfect Nash equilibrium for the both cases $\bar{g_2}\ge \...
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Game of Price Gouging (1st Degree PD)

I am currently modeling a game that shows price gouging is socially beneficial under the right conditions. The question is, I am only evaluating one good and not the classic two good case, so should ...