# Tag Info

17

Traffic reports are another type of information that potentially makes everyone worse off. A recent working paper (Wiseman and Wiseman 2019, https://drive.google.com/open?id=10B6VudYJOQB5w2UVBrYEjYc5wwzGZc8Z) shows this in a simple model of traffic. I quote from the paper, "...public information about road conditions tends to increase average travel time ...

11

This sounds glib, but The Internet is an ongoing example. In economic models where access to information is an explicit factor, we often gloss over the fact that mere exposure to information about the state of the world is not enough to improve welfare - one also needs the cognitive skills to use those facts to develop plans in support of preferences, and ...

10

The “to be announced” or TBA market for agency mortgage-backed securities is a great example of this. The short version is as follows: The TBA market is a market wherein one can purchase or sell for future delivery pools of mortgages that conform to certain characteristics (e.g., and to vastly simplify, 30 year mortgages at a 4.5% coupon) without ...

8

The post of @Mmmmmm about traffic reminded me of Braess's Paradoxon: There are situations in a traffic network (under the assumption that all drivers are rational) where removing some roads leads to a lower average amount of time spent driving. While the paradox itself was constructed with another goal in mind it assumes that all drivers know the optimal ...

8

If in equilibrium, a player "chooses a mixed strategy" that plays $H$ and $T$ with positive probability, $H$, and $T$ must be both optimal choices. It is a standard result that for a (subjective or objective) expected utility maximizer, randomizing can only be optimal if it is over pure optimal choices. This is a direct consequence of expected ...

6

There are a lot of game theorists quite open to many versions of behavioral economics. That being said, I think there are some reasons why these are still fairly separate areas. I will focus in particular on the issue of rationality. Parts of behavioral economics simply do standard economics with somewhat different preferences, such as other-regarding ...

6

Disclaimer: My academic coming of age was in an environment where behavioral economics played only a minor role. My research is theoretical, both "behavioral and non-behavioral", economics. I believe it is incorrect to say that game theorists (or economists) in general are not convinced by behavioral economics. You can easily see it is considered ...

6

This statement is wrong. Consider Alternating Matching Pennies with imperfect information (the follower doesn't observe the leader's move). The strategic form of this game is just the classical (simultaneous-move) Matching Pennies Game and the unique NE has both players mixing.

6

If you draw the corresponding game tree, you will see that "equivalent to simultaneous move game" implies that the game has no proper subgame and the only subgame is the whole game. This is because the information set of the second player covers every move of the first player. Therefore, every Nash equilibrium is trivially also subgame perfect.

6

It's well known that if $\succsim$ satisfies independence, then it is also convex. Since $\succsim$ satisfies independence, $L\succsim L^{'} \iff \alpha L+(1-\alpha)L^{''}\succsim \alpha L^{'}+(1-\alpha)L^{''}$ for all $\alpha \in [0,1]$ and $L, L^{'}, L^{''}\in \mathfrak{L}$ Convexity requires: $L\succsim L^{''}$ and $L^{'}\succsim L^{''} \... 6 A couple hints. Regarding the lower bound on$\epsilon$: What happens if deviation occurs at stage$T$? In other words, there is no opportunity for your so-called "punishment stages". Regarding the upper bound on$\epsilon$: Suppose player 2 deviates at stage$T-1$but player 1 does not. What must be true about$\epsilon$in order for player 1 to ... 5 Is there any more information about why von Neumann had this attitude? There must be, but I have never seen it. Or can we infer a reasonable answer? Here is one possibility based on hearsay among the Game Theory community. Von Neumann thought that there was a sharp distinction between zero-sum games and other games. In zero-sum games, there was no ... 5 How can someone claim that this return is guaranteed, since we need to use$\mathbb{V}ar(\widetilde{W})$to measure the utility gain of an individual? Maybe I misunderstand your point, but though$\widetilde{W}$is a random variable,$\mathbb{E}(\widetilde{W})-\frac{\rho}{2}\mathbb{V}ar(\widetilde{W})$and hence$CE(\widetilde{W})$is a real number. So$CE(...

5

There is a series of papers that address precisely this question. The most famous ones are probably Walker and Wooders (2001) and Chiappori, Levitt, and Groseclose (2002) that deal with penalty kicks and tennis serves. Both papers conclude that the behavior of professional athletes is consistent with them playing g a mixed strategy equilibrium. A more recent ...

5

Level-k reasoning in the stag hunt game is analyzed in Gracia-Lázaro, Carlos, Luis Mario Floría, and Yamir Moreno. "Cognitive hierarchy theory and two-person games." Games 8.1 (2017): 1. The idea that playing $s$ guarantees its payoff is discussed in Aumann, Robert "Nash equilibria are not self-enforcing, in ‘‘Economic Decision-Making: Games, ...

5

The following two claims hold in the general $n$-shop case. Claim 1. In equilibrium a shop closest to an edge (0 or 1) cannot be alone. Proof. Such a shop could gain customers by moving slightly inward. Claim 2. In equilibrium at most two shops can be in any location. Proof. Assume there is an equilibrium where there are three or more shops in a location. ...

5

$U^S(\bar y,\bar m,b)=\max_{y\in Y}U^S(y,\bar m,b)$ is standard notation that says $\bar y$ is the action (taken by receiver) that would maximize sender's utility given message $\bar m$ and bias parameter $b$. In other words, sender would prefer receiver to choose $\bar y$ when he sends message $\bar m$. Sender's maximized utility is $U^S(\bar y,\bar m,b)$. ...

5

As is clear from the answer of VARulle, complete information is of no use. Every (finite) game in normal-form is the normal form of an extensive form game of complete information. The situation is different for games of perfect information, and one can prove a result to the effect that "Almost all finite games of perfect information have equilibria that ...

5

The real-life question is "how do you persuade people to use mixed strategies"? To stick with your example, Consider a person that has to make a binary choice $(H, T)$, and, after contemplation, they conclude that the optimal strategy is the mixed strategy $(2/3, 1/3)$. I have never know of anyone putting two red and one blue ball in a vase and ...

5

Since you mention IEWDS, I presume by "dominant" you actually mean "dominated". Any strictly dominated strategy would satisfy the condition defining weakly dominated strategies and hence be called such. And yes, strictly dominated strategies can (and should) be eliminated in the process of IEWDS. The possible typo notwithstanding, any ...

5

There is also no NE which sustains coopration for more or less the same reason as in the SPNE case. Consider, a PD played twice. A strategy contains five actions, one for each decision node: one in the beginning (empty history) and one for each of the four period-2 histories (CC,CD,DC,DD). I claim that any strategy other than (D;D;D;D;D) is dominated. ...

4

The Nash bargaining solution DOES maximize the Nash product. You have to separate the playing of the game from the bargaining problem. If the players negotiate a binding agreement they will realize that their maximal total payoff from playing the game is $3$. This can be achieved by playing $(T,L)$ or $(T,C)$, or any mixture of those two profiles. The ...

4

Paul Krugman recently discussed the Bloomberg terminal, a classic example of a resource with the following properties: Those who get it are at an advantage, so naturally everyone gets it; It's not free, so everyone getting it cancels out the benefits, making even worse off. The world must be full of examples of this. Dave Gorman once mentioned another ...

4

The solution concept of Bayes Correlated Equilibrium applies to games, viz strategic interactions, between multiple players. Thus, in a single person decision problem its use seems to me inappropriate or at least superfluous. A lot of effort has been spent over the last 70 years (dating back at least to Blackwell 1951, 1953) to explore the notion of ...

4

Claim: If choice sets $T, M,$ and $A$ are finite, then an assessment $\{\beta^*_{r}, \beta^*_{s}, \mu^*\}$ is a WPBE (weak perfect Bayesian equilibrium) of the two-stage signalling game between receiver $r$ and sender $s$ if and only if it is a SE (sequential equilibrium). Proof: SE $\implies$ WPBE is trivial since SEs are PBEs by construction, and thus are ...

4

For most purposes, there is no difference between (two-player) zero-sum and constant-sum games. One usually assumes in game theory that players maximize expected utility. Payoff functions are von Neumann-Morgenstern utility functions. One does not change the preferences induced by such a payoff function if one adds or subtracts a constant. One can, therefore,...

4

As Michael Greinecker noted, the stag hunt is the leading example of a symmetric 2x2-game with a payoff-dominated but risk-dominant NE. In symmetric 2x2 coordination games, a pure NE is risk dominant iff it is the unique best reply to the mixture $(\frac12,\frac12)$. Since Level-0 types are usually assumed to mix uniformly over pure strategies, all higher-...

4

At the intersection of differential equations and game theory one can find differential games. Arguably, the most famous applications of differential games are in warfare, e.g., the homicidal chauffeur problem. However, not all differential games are of the pursuit-evasion kind. Whoever wants to learn differential games may wish to learn optimal control ...

4

I know a bunch of people who teach behavioral economics using Erik Angner's book. I love Rani Spiegler's book on behavioral economics in IO called "Bounded Rationality and Industrial Organization." Both books will introduce models that can be applied to poker. Perhaps a little lighter but still scientific readings would be Kahneman's "Thinking,...

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