Questions tagged [dynamic-games]
Questions related to the application of game theory to situations in which actions are taken sequentially.
48
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Finding strategies and subgame perfect equilibria
In my game theory class we recently learned about dynamic games and I wanted to know whether I solved my homework problem correctly (and how to attempt the second part).
a) Determine all strategies ...
- 101
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0
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12
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Dynamic price competition with capacity constraints
I have a dynamic price (Bertrand) competition with 2 players with the same capacity constraints. Grim trigger strategy is to set monopoly price at t=0 or if the monopoly price was set by both players ...
- 21
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vote
1
answer
105
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Profit Maximizing with a competitive fringe
I have this question:
Your business is the dominant firm but there exists a competitive fringe.
The competitive fringe produces with total cost: $\; c_𝑓(q_f) = 3𝑞_f$.
There have also been some ...
- 21
1
vote
1
answer
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Extensive Form of Games
Is there any reason for the differing shapes of game trees when we use extensive form representation? For instance, why does the job market signalling game and the repeated Prisoner's Dilemma take the ...
- 35
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18
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PBE solution strategy
I am not comfortable with dynamic games of incomplete info. I am trying to solve the example at https://pubs.aeaweb.org/doi/pdfplus/10.1257/jel.54.2.442 , but can't even come up with a good strategy. ...
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99
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Perfect bayesian equilibrium on and off the equilibrium path
I know that Bayes's rule can verify the first perfect bayesian equilibria. I am more uncertain about the second perfect bayesian equilibrium, which is off the equilibrium path.
Any help would be much ...
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36
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One shot-deviation property for games of imperfect information
The equivalence between subgame perfection and one-deviation property is typically stated for games of perfect information (where information sets are singletons). Does the Blackwell-style argument ...
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45
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Sequential version of all-pay auction
Sequential version of the all-pay auction. Two bidders alternate in bidding. A prize of \$5 is auctioned. At each move of the game, the bidding player decides whether to raise the current bid by \$1 ...
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284
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Subgame perfect Nash equilibrium when there is a tie in payoffs seems problematic
My question follows from this question: https://math.stackexchange.com/questions/2132846/game-theory-subgame-perfect-nash-equilibrium-in-a-sequential-game-with-identica from Maths stackexchange.
Based ...
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1
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58
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Relation between Markov Perfect Nash Equilibrium and Markovian evolution of the state
I am studying dynamic games and I'm fundamentally confused about the relation between Markov Perfect Nash Equilibrium and Markovian evolution of the state. Before illustrating my doubt, let me ...
- 426
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Why Sequenial Equilibrium (SE) imposes no restrictions on the off-equilibrium beliefs in the Spence's model?
I read some lectures on the Spence's model. Some (see e.g. P31 of lecture PPT from MIT game thoery course) mention that SE imposes no restrictions on the off-equilibrium beliefs but without proof. I ...
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Design of efficient cheap talk communication
Are there any papers about efficient cheap talk communication, where the players achieve the equilibrium payoffs of a correlated strategy as in Aumann's seminal paper? Or in case no such paper exists, ...
- 959
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1
answer
65
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Correlation device that induces a specific transition probability
Taking a look at this paper of Forges and Vida the authors define a correlation device in page $102$, that is a standard probability space $\left(\Omega,\mathcal{B},\mu\right)$, They assume that the ...
- 959
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answers
53
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Repeated Games of Incomplete information set up and questions
The following are from the model of Jérôme Renault (Repeated Games of incomplete infomration).
The preliminaries of the model
Formally, a repeated game with incomplete information is given by the ...
- 959
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39
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Perfect recall vs perfect monitoring
Following my previous previous post here, I would like to add another question. Is perfect recall the same with perfect monitoring? If not, what are their differences?
- 468
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1
answer
87
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Perfect recall assumption
When we assume that the players can recall perfectly everything about the previous stages of a game, in essence we assume that they know the history path that they followed until they reached to some ...
- 468
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0
answers
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Definition of the space of a repeated game
I want to define the space of a stochastic game and it confuses me a lot, so I want someone to check please the space $\Theta$ that I define at the end and how could I define the sigma algebra of this ...
- 468
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answers
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How to define a dynamic programming problem in an incomplete information game?
How can I define a problem of dynamic programming, to use the Hamilton-Jacobi-Bellman equation in order to solve the utility maximization problem of the generic agent of a dynamic game with incomplete ...
- 468
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answers
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Strange screening game were FS contracts equals optimal contracts
Consider the setting where a principal hires an agent to do a project. Payoff from project is $\pi = \beta e$, where $\beta \in \{1,2\}$ is the degree of the agent's talent and $e \in [0, +\infty]$ is ...
1
vote
1
answer
776
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Simultaneous vs Sequential Games [closed]
Is there a way to characterize the distinction between simultaneous vs sequential games? I'm trying to describe a situation where players can only take actions without knowledge of other players' ...
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4
votes
1
answer
183
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Finitely repeated Prisoner’s Dilemma with switching cost
I'm doing this finitely repeated Prisoner's dilemma with switching costs but I have trouble showing the fact that $\varepsilon$ had to be $1 < \varepsilon < 2$. I do see why and that it is a ...
- 105
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0
answers
184
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Fehr-Schmidt, Ultimatum game, Subgame-Perfect Nash Equilibrium
I'm studying the different variations of the ultimatum games. I've spent some time on this following game:
Assume now that each player does not only care about the amount of money she receives, but ...
- 105
2
votes
2
answers
528
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Pure-Strategy Bayesian Nash equilibrium with general common prior
I'm doing a problem set on the subject of Bayesian Nash equilibrium. I'm asked to find the pure-strategy BNE of the following. I've calculated to matrix shown below. My first concern is if I've ...
- 105
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votes
1
answer
100
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Estimation of point-identified Dynamic Discrete Choice models with moment inequalities
I'm trying to understand and implement in code the method in Bajari, Benkard, Levin (2007). The first stage is clear to me, as well as how to forward-simulate to obtain an estimate of the value ...
2
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4
answers
128
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How to achieve the best outcome by a single statement in this game?
This game is taken from Schelling's Game Theory: How to Make Decisions by R.V. Dodge, in which contenders practice brinksmanship to their own advantages. It goes as follows:
Anderson, Barnes, and ...
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votes
1
answer
163
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Sequential Game is Extensive form game?
Dynamic, Sequential, Stochastic, Extensive form and Evolutionary games.
I know what all of them mean very roughly.
I want to clarify them.
As I understand Extensive form is a description of a ...
- 165
2
votes
1
answer
127
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Definition of subgame perfect Nash equilibrium
Take a two-stage game with complete information and simultaneous actions in each state:
(1) Player 1 and 2 simultaneously choose action $a_1\in A_1$ and
$a_2\in A_2$ respectively.
(2) Player 1 and ...
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votes
1
answer
311
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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 ...
- 383
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votes
1
answer
329
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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 ...
- 401
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votes
1
answer
432
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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 ...
- 401
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vote
1
answer
280
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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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1
answer
804
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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 ...
- 155
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votes
0
answers
236
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Subgame Perfect Equilibrium with Pure Strategies in Sequential Games [closed]
If I have a sequential game, i.e. in each node (that I will call $t$) only one player choose an strategy from a finite space of strategies, Is it true there always exist a subgame perfect equilibrium ...
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2
answers
154
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Price setting firms with cost reduction technology
As part of my undergraduate studies in Industrial Economics, I am trying to solve the following question:
Two price-setting firms are competing in a market for a homogeneous product. There are 10,...
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votes
1
answer
125
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Extensive Form Games
( The game of “ chicken”) Two cars are driving at each other at great speeds.
If nobody changes directions, in 3 seconds they will collide and die a gruesome death,
yielding payoffs of −100 for both ...
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1
vote
1
answer
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World as a society of interlinked multiplayer individuals
If you were to take a game-theoretic model of a world in which each individual tried to optimize their utility function / goals then how would you go about designing a computer simulation of the ...
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0
answers
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Dynamic dividing a dollar game
The question is a reformulation of an incomplete version.
Consider the following dynamic dividing a dollar game where agent 1 claims $x(t)$ of the dollar and agent 2 $y(t)$ (paper).
\begin{align}
&...
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Dynamic contract theory: Demarzo, Fishman(2007) optimal long term financial contracting
I am reading Demarzo, Fishman(RFS,2007). Any suggestion will be appreciated. My questions are the following:
(a)
\begin{equation*}
b_T^e(a) = \left\{\begin{array}{lll}
-e^{(\gamma-r)(...
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votes
1
answer
71
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Terminology for "part" of extensive form game
How should I call a "part" of an extensive form game which is neither (i) a subgame, nor (ii) a stage in a repeated game?
For instance, consider the class of games constructed by "stacking" 2 ...
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answers
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Multiple equilibria: which one to select?
There are two agents $i=1,2$. Consider the following programm
\begin{align}
&V_1(x_0) := \max_u \int^\infty_0 e^{-\rho t}F_1(x(t),u(t),v(t))dt\\
&V_2(x_0) := \max_v \int^\infty_0 e^{-\rho t}...
- 1,559
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votes
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answers
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Converging Trajectories and Sufficiency for Optimality
(The question is loosely relatet to this thread.)
In the paper "Feedback Equilibria for a class of non-linear Differential Games" by Mäler et al. it is stated (p. 14)
In fact sufficiency is ...
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0
answers
103
views
Can repeated bidding in an auction make each player's type common knowledge?
In Benjamin Edelman, Michael Ostrovsky, and Michael Schwarz(2007), there's a hand-waving argument to justify their setting as a game of complete information:
we assume that all values are common
...
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7
votes
1
answer
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How to verify Value Function in nonzero sum two player Differential Game?
There are two agents $i=1,2$. The state $k$ is governed by $\tau_i\in[0,1]$ where
\begin{align}
\dot{k} = f(k,\tau_1,\tau_2).
\end{align}
Define the value function of player $i$ by
\begin{align}
v_i(...
- 1,559
9
votes
1
answer
373
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What does Battigalli really mean by "Players can not choose strategies, they can only choose actions."?
In this video (from 7: 30 to 9: 00)on Youtube, Battigalli mentions the state of world for a simple three-legged centipede game, which, in his own word, is
"$\ldots$a description of everything ...
- 1,416
5
votes
2
answers
148
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Repeated games without a beginning and an end
I'm interested to know results on repeated games indexing each stage game by $\mathbb Z$ which contrast with those indexed by $\mathbb Z_+$.
It seems to me this could be quite different from repeated ...
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votes
1
answer
257
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Models for online markets with reputation system
The only relevant model I'm aware of is Liu Qingmin(2011 R.E.S). Is there any other decent models dealing with the mechanism of online markets under reputation system, and perhaps linking to ...
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votes
2
answers
793
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One-shot deviation principle for infinite repeated games and dynamic programming
In a context that future return is discounted by a constant parameter, one-shot deviation principle holds for both repeated games and dynamic programming.
Because, in repeated games, a one-shot ...
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8
votes
1
answer
368
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Identification with BBL
In the last few years, the estimator proposed by Bajari, Benkard, and Levin ('07) for dynamic games has been gaining popularity. It is relatively straight forward and is one of the only viable options ...
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