1
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1answer
58 views

Economic Applications of Game Theory

I'm currently looking at this course in economic game theory. However, when attempting this example: In this question you are asked to price a simplified version of mortgage-backed securities. ...
1
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1answer
41 views

In Courty and Li (2000) “Sequential Screening”, what justifies the last equation in Lemma 3.2?

Regarding the article "Sequential Screening," in Review of Economic Studies, 2000 by Courty and Li: In Lemma 3.2, the last equality states that ...
4
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1answer
50 views

Expected revenue obtained by the Vickery auction with reserve price $1/2$

I would like to prove that the expected revenue of the Vickery auction with reserve price $1/2$ is $5/12$ when there are one item and two bidders the distribution of valuations are uniformly between ...
1
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2answers
70 views

Third and average price auction

Third price auction: the winner is the highst bidder but this time instead of paying the second highst bid, he would pay the third highst bid. -assume there are at least 3 bidders. - Average price ...
0
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1answer
66 views

Game Theory in relation to economics and sociology [closed]

I know some algebra and calculus, and have been reading about Linear Programming/Game Theory. How are the models in this field, even the infinite calculus models, usable in macro economics. Even ...
4
votes
3answers
184 views

How practically relevant is game theory?

I usually don't care too much about the practical relevance of nice mathematics :-) But this time, as I am looking to find some areas where I can apply maths and possibly collaborate with ...
2
votes
3answers
145 views

Precise definition of a “game of incomplete information” (Game Theory)

Question: In game theory, what is the precise definition of a "game of incomplete information"? What I've found so far: In the standard first year graduate economics textbook on microeconomics ...
0
votes
0answers
110 views

Robinson Crusoe economy problem

Consider the Robinson-Crusoe one-consumer, one-producer economy. Compute the equilibrium prices, profits and consumption when the production function is $f(L)=\sqrt{L}$, the utility function is ...
2
votes
1answer
103 views

Brouwer's fixed point theorem

Theorem: If $f:D^n\rightarrow D^n$ is continuous then there is $x \in D^n$ such that $f(x)=x$. To prove the theorem we assume that $f$ is cts but has no fixed point, that is $f(x)\neq x$ for all ...
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2answers
84 views

Why should a GE fail to exist in non-convex sets?

In an exchange economy with $2$ goods and $m$ identical Households where each household has utility function $u(x_1, x_2)$, together with positive endowments. If preferences are not convex, then why a ...
1
vote
1answer
67 views

Implications of axioms of expected utility theory

Axioms for Expected Utility: Let $\succ $ be a binary relation on $X$. A1. $\succ $ is asymmetric and negatively transitive. A2. Independence of Irrelevant Alternatives: If $p,q,r \in X$ and if ...
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votes
1answer
19 views

Understanding a component of an equation of finite game repetition

I have the following equation: T = total times the game is repeated t = current period delta = discount rate u_i(a_i^t...) = the state payoff to player i I'm attempting to understand the ...
0
votes
1answer
210 views

Question related to the General equilibrium in exchange economies

I need some help in solving this question: Consider the following two-person, two-good economy. Persons $A$ and $B$ each consume two goods xylophones $(x)$ and yams $(y)$. Person $A$ enters the world ...
2
votes
1answer
90 views

Generalized Mechanism Design, Stanley Reiter diagram and Vickrey Auction

I am trying to learn this new topic, Mechanism Design and stumbled upon the "Stanley Reiter" diagram (see the top-right side on the page). I have also learned that the Second Price Sealed Bid ...
2
votes
1answer
307 views

questions on information set definition

The definition of "information set" is An information set is a set of decision nodes, all belonging to the same player, over which that player cannot distinguish. ...
1
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1answer
111 views

Two traders don't trust each other; what transactional equation optimises reward and minimises risk?

Years ago while on a Wikipedia browsing binge, I read a maths article about how two (or more) mistrusting parties can reach an transactional equilibrium, but I've wracked my brain and I can't remember ...
4
votes
1answer
83 views

Shapley value: an alternative representation

It is my belief that the more common representation of the Shapley value is given by $$ \phi_i(v)=\sum_{S\subseteq N-i} \frac{|S|!(|N|-|S|-1)!}{|N|!}(v(S\cup\{i\})-v(S)) $$ where $v \in ...
1
vote
1answer
179 views

SPNE of infinitely repeated game

Let $G$ be a game with finitely many players and $\underline{v}= (\underline{v}_i)$ be the minmax payoff profile. Denote by $G_{\infty}(\delta)$ the infinitely repeated game whose stage game is $G$ ...
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0answers
83 views

Optimal auction for risk averse seller

Consider an auction of a single unit of indivisible good. There are $n$ buyers whose values of the object is drawn independently from the uniform distribution on $[0,1]$. The buyers have interim ...
3
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2answers
223 views

Exercise in Mechanism Design

I found an exercise with solution in the field of Mechanism Design. The problem is I don't understand the solution. Exercise. Use the characterization of incentive compatible direct-revelation ...
4
votes
3answers
126 views

Is there any research field dedicated to estimating a “game” itself in game theory?

Game theory stuffs usually provide how a "game" works and then tries to figure out solutions - but I am wondering if there is any research field dedicated to estimating the full rules of a game. So ...
5
votes
1answer
183 views

When do $\epsilon$-Nash equilibrium strategies converge to Nash equilibrium strategies?

Suppose I have a game on $n$ players and a sequence of strategy profiles $(s_1^{(1)},\dots,s_n^{(1)}), (s_1^{(2)},\dots,s_n^{(2)}), (s_1^{(3)},\dots,s_n^{(3)}), \dots$. Each ...
3
votes
1answer
124 views

Existence of asymmetric equilibria in the dollar auction game

Consider a game in which an auctioneer sells one dollar to the highest bidder. The high bidder wins the dollar, but every bidder pays their bid. Concretely, assume that there are two bidders ...
3
votes
1answer
74 views

Stability under supremum of sets of social choice function with single peaked preferences

Here is a question emerging from reading Moulin, H. (1980). On strategy-proofness and single peakedness. Public Choice, 35(4), 437–455. The setting is as follows: A non-empty finite set of ...
0
votes
1answer
95 views

Using limit argument with non-continuous social-choice functions

This question is related to another question of mine Invariance of strategy-proof social choice function when peaks are made close from solution, and it revolves around the use of limit arguments with ...
6
votes
1answer
119 views

Invariance of strategy-proof social choice function when peaks are made close from solution

A question emerging from reading Schummer, J., & Vohra, R. V. (2002). Strategy-proof Location on a Network. Journal of Economic Theory, 104(2), 405–428. The setting is as follows: A finite set ...
1
vote
1answer
49 views

Concept of efficiency in auctions

I have some confusions about the concept of "efficiency" in auction theory. One interpretation is that an auction is efficient if it maximizes the social-welfare. But social-welfare is not well ...
4
votes
2answers
105 views

Does Arrow's Theorem apply when choosing a single best candidate?

According to Wiki, Arrow's Impossibility Theorem proves that we cannot create a social welfare function that obeys unanimity, non-dictatorship, and IIA. However, in real elections, we want to choose ...
0
votes
1answer
131 views

Find profit maximizing profit and quantity given willingness to supply curves and a merger

This is a homework problem, but I'm at my wit's end. I don't even know where to start on this, but I've tried a number of strategies. Consider a regional market for wholesale electricity where ...
2
votes
2answers
2k views

Cournot-Nash Equilibrium in Duopoly

This is a homework question, but resources online are exceedingly complicated, so I was hoping there was a fast, efficient way of solving the following question: There are 2 firms in an industry, ...
4
votes
1answer
484 views

Gibbard–Satterthwaite Theorem versus Arrow Theorem

Arrow Theorem is a very classical result in social choice theory, stating very roughly that any reasonable voting procedure is either dictatorial or subject to tactical voting. More precisely, there ...
1
vote
0answers
85 views

Game theory question- information quality maximisation, opinions of the question

I am developing a game theory question to help in deconstructing situations where information quality is comprimised and requires valuation against a set of criteria. I would be interested to know any ...
2
votes
0answers
168 views

What is the (expected) outcome of this hybrid auction?

A certain hybrid auction can be accurately modelled as follows. There are $n$ risk-neutral, rational participants $i=1,2,\ldots,n$, and a guy called Zerro: $i=0$. Each, except Zerro, has a private ...
4
votes
1answer
739 views

Finding mixed Nash equilibria in continuous games

I'm taking my first (graduate-level) game theory class. I understand how to find Nash equilibria in simple games, such as those given in finite tables, and can see (usually) how to find the mixed ...
1
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2answers
363 views

Game theory: Nash equilibrium in asymetric payoff matrix

I have a utility function describing the desirability of an outcome state. I weigh the expected utility with the probability of the outcome state occuring. I find the expected utility of an action, a, ...
1
vote
1answer
129 views

Mathematics behind Incentive Design

I was working on an Applied Math project on allocation and I had an interesting idea about extending it to providing incentives to different "players" in the allocation process. But I am clueless ...
2
votes
1answer
145 views

vickery auction question(second-price auction)

The question is as follow, Alice and Bob would both like to own the same manuscript. The manuscript is worth 5 million to Alice and worth 3 million to Bob. The present owner of the manuscript ...
0
votes
1answer
230 views

subgame perfect nash equilibrium for war of attrition

the question is as follow: suppose that two players are playing war of attrition, that means both of them could choose either to fight or quit, if either one of them quit, the game ends, and if ...
1
vote
2answers
3k views

cournot competition with N-firms

The question is as follow: Here is how we can think of N-firm Cournot competition. Assume all the firms have the same marginal cost C > 0. Firm 1 chooses Q1, Firm 2 chooses Q2, and so on. The market ...
1
vote
1answer
152 views

Cournot-game problem

I'm so stuck with an exercise about Cournot game and was hoping if someone could help me out here. Would appreciate all the help. This is the exercise: Consider the market for Blue Turtle (a new ...
3
votes
0answers
121 views

Optimal strategy in a VCG auction with partial collusion?

Suppose you control the bid prices in a multiple-item VCG auction for a partial coalition of bidders. Each bidder is only allowed to win one item out of the set of multiple items, which are all ...
1
vote
1answer
213 views

Question on mixed nash equilibrium!

The question is as follows: Think of the Golden Ball game. Now player 1 is money-minded and jealous, and player 2 is very good-hearted, so the payoff matrix is follows: ...
2
votes
1answer
136 views

Economics: two rival firms in two countries

I am currently working on a paper in macroeconomics, where I found a result that I cannot manage to understand. Since we don't have a macroeconomic site yet, and this is mostly game theory, I will ...
2
votes
0answers
108 views

proof using (fixed point theorem)

I am seeking to solve for a Nash equilibrium in pure strategies $(d_2,d_2)$ involving two players, $1$ and $2$. Given that $h'(.)$ is s strictly decreasing and continuous function, $\Phi(d_1-d_2)$ ...
0
votes
2answers
627 views

Subgame Perfect Nash Equilibrium

My homework question is summarized below: There are 7 players (say P1,P2,...,P7) trying to split 100 dollars. The game starts with P1 proposing an allocation of the 100 dollars to each ...
5
votes
1answer
274 views

Olympic Badminton, or How to Design a Tournament

Hearing the recent news about disqualified Badminton players in the ongoing 2012 London Olympics got me wondering about how best to design tournaments to avoid situations where players are ...
0
votes
1answer
727 views

Finding Nash Equilibria with Calculus

The problem is summarized as: There are two players. Player 1's strategy is h. Player 2's strategy is w. Both of their ...
1
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1answer
869 views

Unable to find Nash equilibria in mixed strategies

Here is the strategic form game: Player 2 Left Middle Right Top 2,2 0,0 1,3 Player 1 Middle 1,3 3,0 1,0 ...
1
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2answers
224 views

summation notation for general sets

I'm working through an academic game theory paper and stumbled upon this summation notation in a proof and I'm not quite sure what it means: $$\sum\limits_{j \in M \backslash\ \{i\}}$$ There is a ...
1
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1answer
172 views

Nash equilibria of mixed strategies

I am given the following game to find nash equilibria in pure and mixed strategies: $\begin{pmatrix}& & Litte John &\\ & & c & w \\Big John & c & (5,3) & (4,4) \\ ...