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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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Modeling technique: the choice between a cutoff Strategy or a mixed Strategy

In some cases, a model can be expressed using either a cutoff strategy or a mixed strategy. The example of cutoff strategy is that a player's cost of using a strategy is distributed to according to ...
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Stay or switch game

Consider a game consisting of two players, P1 and P2, played over multiple time steps. Refer to P1 as she and P2 as he. State: Each player can be at one of two locations, A or B. Writing the possible ...
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Clarification on the definition of Bayes Correlated Equilibrium

I would like your help to understand the definition of Bayes Correlated Equilibrium (BCE) in an incomplete information game at p.7 of this paper. Let me summarise the definition provided in the paper....
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Stackelberg Oligopoly 3 firms

Imagine that there are 3 firms in a monopolistic market, F1, F2 and F3. Firms 1 and 2 are incumbent firms and act simultaneously whereas Firm 3 observes the actions of both firms before deciding ...
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Implications of the concepts of combination/expansion of an information structure

I would like your help to understand the concept of combination/expansion of an information structure in the incomplete information game at p.6-9 this paper. Let me summarise the game as described in ...
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1answer
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Sequential game equilibrium strategy question

The question asks for player B's equilibrium strategy, hence shouldn't player B choose the strategy that gives the highest payoff after player A's move? Why does player B choose 4 over 5 and 6 over 8 ...
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Optimal pareto in two-person game

For what values $x$, $y$ the profile $(D,L)$ is Pareto optimal? \begin{array}{c|ccc} & L & R \\ \hline U & x,5 & x+2,y \\ D& 1,-1 & x,0 \\ \end{array} Is correct $x<1$ ? ...
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Condition for a Nash equilibrium

Consider two people have a mutually advantageous relationship. That is, if both dedicate more effort to the relationship both improve. Specifically, each individual chooses a level of effort $x_{i}\...
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1answer
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Construction of a 3x3 simultaneous game

How could I construct a 3x3 simultaneous game with 2 players with no equilibrium in pure strategies but 1 is mixed strategies . I am able to write down one with no pure strategy Nash equilibrium but ...
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Asymmetric Nash Bargaining

The Nash bargaining solution selects the unique solution to the maximization problem $\max_{s_1, s_2 } (s_1 - d_1) (s_2 - d_2)$ such that the solution satisfy the following axioms : Invariance ...
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1answer
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Rationalizability or Nash equilibrium

In the 'chicken' game, (stop,go) and (go, stop) are the two pure strategy Nash equilibrium profiles. If the game is played once, does it make more sense to use the rationalizability solution concept? ...
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1answer
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Credible Threat in the Perfect Bayesian Equilibrium

Consider a simple game between P1 and P2 shown in Figure 1. We consider a Perfect Bayesian Equilibrium. P1 uses a cutoff strategy based on his $c_1$ that has the Cumulative Distribution Function of $...
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What is the game theory of retaliatory trade tariffs?

Suppose no tariffs, or negligible tariffs, exist between nations A and B, and suddenly A introduces substantive tariffs on certain products A imports from B. In theory, this could lead to B and A ...
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The concept of expansion of an information structure

I would like your help to understand the concept of expansion of an information structure in the incomplete information game at p.6-9 this paper. Let me summarise the game as described in the paper. ...
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2answers
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The concept of information structure in incomplete information games

I would like your help to understand the concept of information structure in the incomplete information game at p.6-7 of this paper. Let me summarise the game as described in the paper. There are $...
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1answer
135 views

Bayes Correlated Equilibrium: obedience

I would like your help to understand the definition of obedience in an incomplete information game at p.7 of this paper. Let me summarise the definition provided in the paper. There are $N\in \...
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1answer
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mixted strategy that assigns positive weight to a pure startegy that is dominated

This problem is of Fernando Vega Redondo(Economics and the theory of games) Exercise 2.1 Let G be a game in strategic form. Prove that, for every player $i\in N$, every mixted strategy $\sigma_{i}\...
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1answer
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Are there strictly dominated strategies?

Two players simultaneously announce a prime number less than 20.Denoting $p_{i}$ the number announced by the player $i$, the payoffs are: -If $p_{1}+p_{2}<14$ each player receives as payment the ...
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Obligations of a company

Any company may "feel" obligated towards several parties at once: its shareholders its employees its customers its partner companies (sub-contractors and suppliers) its country and social environment ...
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1answer
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Is anyone familiar with the following basic resource sharing model?

Here is a resource sharing model, I do not remember where I came across it, I am wondering if this is well known in econometrics. Let $T > 0$ be the total quantity of resources. For example, ad ...
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Interpretation of Solution Concepts

I was wondering whether there is a neat overview over different interpretations of game theoretic solution concepts such as Nash equilibrium, Sequential Equilibrium and the like. Textbooks I found ...
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1answer
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Is truth cheap, and falsehood expensive and volatile? [closed]

Question: In a scenario where data is bought and sold in a double-auction market, will the trading price and volatility of a given piece of data become inversely proportional to its accuracy over ...
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2answers
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Game Theory: finding nash equilibria of an extensive form game (game tree) [duplicate]

How do you find the pure Nash equilibria from this commitment game? The SPNE is (U, ps) Do you find the NE by finding the best response (BR) of a player to a specific strategy of the other player? ...
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How to approach such question of two periods and asymmetric information game?

There are two players 1 and 2, playing a two-period public good contribution game. The benefits from the public good per-period to each player is $b_1$ and $b_2$ respectively, which are common ...
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1answer
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Bayesian Nash Equilibria in Battle of Sexes

Consider the static Bayesian game as described above. $\ t_1$ and $\ 𝑡_2$ are the types of the row and column player respectively, which are both uniformly distributed on the interval [0,1]. The ...
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1answer
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Symmetric Cournot equilibrium: suffciency without second order conditon

Let $q_i \in Q = \mathbb R_+$ denote the quantity produced by firm $i \in \{1,2\}$. Further let $\pi_i(q_1,q_2) = (1-q_1-q_2)q_i$ denote the profits of $i$. A Nash equilibrium $(q_1^*,q_2^*) \in Q^2$ ...
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Is second price auction better than first price sealed bid auction? Why? [duplicate]

As I understand and have read the advantage of the 2nd price auction is that it encourages bidder to bid for 'true value', which I think can also be done with the 1st price sealed bid auction. I might ...
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1answer
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Cournot's game profit maximisation first order condition question

My question is about the last part (I attached the rest for context). I don't understand the final line at all. I thought the first order condition would just be to set the derivative = 0. Very ...
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1answer
116 views

Definition of Bayesian Nash equilibrium

I have a basic doubt on the definition of Bayesian Nash equilibrium. Consider the following game: 1) $N$ players. 2) Each player $i$ has a type, assigned by nature and denoted by $\epsilon_i$. ...
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1answer
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Spence's Job Market Signaling Game

I have a little doubt in the Job Market Signalling Game. I am referring to A Primer in Game Theory: Gibbons, Chapter 4, Signaling Games The attached paragraph refers to a Separating Equilibrium case ...
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1answer
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Is there a general name for the setup in which payoffs are not known exactly but players try to influence each other's perception of the payoffs?

A recent question elsewhere made me look at the "madman strategy" which actually consists of trying to make the opposite player think that he is playing a game of chicken instead of prisoner's dilemma....
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1answer
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Repeated Game SPNE

I approached this question in this way: $(P_1,P_2), (R_1,R_2), (S_1,S_2)$ are the Nash Equilibria of the Stage 1 game. For the given strategy to be sustained as SPNE, there should be no way unilateral ...
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1answer
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Nash equilibrium - mistake in proof of paper?

I have a question regarding the proof of Proposition 1 in Besley and Ghatak (2007) in Appendix A of their paper. It is a quite highly cited paper but I believe there is a mistake in the proof of their ...
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1answer
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SPNE and Pareto Optimality

"The SPNE of a sequential game might not necessarily be Pareto Optimal" I understand the definitons of Nash Equilibria and Pareto Optimality and that these are not synonymous concepts. An example in ...
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Cournot competition subgame perfect Nash equilibrium with two products

QUESTION: Assume there are two types of products, labelled $l$ and $n$. Firms compete in the market by choosing which product to sell and then choosing the quantities. Let $Q_n$ and $Q_l$ denote the ...
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2answers
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What trick can be used to calculate mixed-equilibria?

In continuous games, the probability distributions over the players' strategy spaces are infinite. How then is it even possible to then derive a mixed-strategy nash equilibrium? One would have to ...
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1answer
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Bayesian Nash Equilibria: Strong and Weak Types

I need a little help with the question. I understand that since both players have two types each, there will be 4 different payoff matrices to be considered, $(S,S)$,$(S,W)$,$(W,S)$,$(W,W)$, each type ...
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1answer
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Are there multiple equilibria in the second price auction?

Suppose that $n\geq 2$ bidders compete in a second price auction. Each bidder $i$ knows their own valuation $v_i$, but only knows the distribution generating the valuations of the other players. ...
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1answer
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Sequential Bertrand game with differentiated goods, how to write the strategies of firm 2 [closed]

In a Bertrand competition with differentiated goods where firms set the prices sequentially, we have the following demand functions: q1 is quantity of goods demanded for firm 1 q2 is quantity of ...
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1answer
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Rationalizable action profiles in nice symmetric games

Suppose we have a nice symmetric game with $n$ players, i.e. each player's action space is the same compact interval of the real line. I am tasked with identifying all of the rationalizable action ...
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1answer
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Screening theory: Bundling problem

Consider an example of a risk-neutral seller that has two distinct indivisible goods for sale. The seller wants to maximize the expected revenue. The buyer's utility is $$I_av_a+I_bv_b-t,$$ where $I_a,...
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1answer
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When solving game theory problems, how can you “assume” that the equilibrium strategy will lead to something happening?

This is something that confuses me a bit when I see my book solve game theory problems. When solving a model's equilibrium (like a subgame perfect nash equilibrium), the book will assume that a ...
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1answer
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Is game theory supposed to be this easy? [closed]

I have a course in game theory coming up, and I decided to look at the curriculum, which is a book by a guy called Gibbons on game theory. I skimmed it, but it seems that the core theory can be ...
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Game Theory Book

I am looking for a book on game theory, but I am not looking for a textbook. What I am after is more of a narrative form book that still provides valuable insights about game theory that I can pick up ...
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2answers
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Can repeated game sustain a discounted average payoff that is not individually rational?

Look at the following payoff matrix, there are two stage Nash equlibria, and we consider a infinitely repeated game with discount factor $\delta\in(0,1)$, can players sustain an average payoff of (2,2)...
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2answers
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What does these “strategy notations” mean?

In a sequential game, where there are 8 pizzas. Player 1 decides number of pizzas he wants. Let's call it S1 (strategy of player 1), and S1 = 5 means player one decided to get 5 pizzas. Then player ...
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1answer
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Necessary indifference conditions in mixed equilibrium

Suppose we are playing a game where the Action set for Player 1 is $(a,b)$, for Player 2 is $(c,d)$, and for Player 3 is $(L,M,R)$. Assume that for Player 3, the action $M$ is weakly dominated by some ...
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1answer
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Non-negative deviations from Nash Equilibrium

I know that in a Nash Equilibrium, no player can profitably deviate from the equilibrium strategy assuming that the strategies of the other players remain the same. My question is, what if a player ...
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2answers
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Questions of the type “What do you think other people would think?”

For a study in the adoption of new technology, a student and I are developing a questionnaire that will poll domain experts on their opinions of what their colleagues would think about benefits/...
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Take It Or Leave It Strategy: Social Optimum

Here is what I understood Using Backward Induction, I inferred that buyer offers a price, say, $P$ and the seller will sell only if $P \geq c(I)$. Setting the lowest possible Price that will ensure ...