25

A concise, completely informal way of putting it is this: The intuitive criterion rules-out any out-of-equilibrium beliefs that can only be correct if some player did something stupid. Below is a slightly more long-winded explanation with an informal example. In many signalling games (that is, games in which one player—the sender—can communicate information ...


17

Two areas that have been profoundly affected by game theoretic research stemming from Nash's contribution are Oligopoly theory There are actually a few examples of what would come to be known as Nash equilibrium in the industrial organization literature that predate Nash's work (for example, Cournot's 1838 analysis of oligopoly competition). However, until ...


14

Sending costly signals may work, at least when the recipient is less attractive than the sender. There's also a nice popular science book by Paul Oyer called Everything I Ever Needed to Know About Economics I Learned from Online Dating that covers some of this ground, including the paper linked above. Another theoretical paper suggests that costly signals ...


14

Nash Equilibrium (N.E) is a general solution concept in Game Theory. N.E is a state of game when any player does not want to deviate from the strategy she is playing because she cannot do so profitably. So, no players wants to deviate from the strategy that they are playing given that others don't change their strategy. Thus, it is a mutually enforcing kind ...


12

You're not alone in your skepticism of the relevance of game theory. Some of the greats, including Gary Becker, were at times dismissive of the practical/empirical importance of game theory (see the introduction/preface of his Economic Theory book). No doubt it is in a way foundational to the economic sciences (see Myerson's great essay on Nash's ...


11

Ariel Rubinstein tends to be insightful regarding these kinds of questions. He addresses the interpretation of mixed strategies in section 3 of this paper. A few possible interpretations aside from deliberate randomization: Purification: A mixed strategy is a plan of action based on information not specified in the model. A fictitious long run story. ...


11

Contracts are a subset of all mechanisms where agreements are enforcable. An example of a mechanism that is not a contract: A second price auction (or Vickrey auction) is a truth-telling mechanism where the enforcability of contracts is not required. In the truth-telling equilibrium no one has any incentive to change their bid, no matter the outcome. This ...


10

This is only half a joke : Nash-equilibrium gives a very good prediction on the relative size of groups of foraging ducks on a pond when two food sources are established at opposite sides of the pond. A very good explanation can be found at https://headbiotech.wordpress.com/nash-equilibrium-example-on-ducks/, among other places (https://headbiotech....


10

This result is indeed a version of Berge's maximum theorem. If there is a continuous function $u:M\times H\to\mathbb{R}$ such that $x\preceq_e z$ if and only if $u(e,x)\leq u(e,z)$, one can derive the result directly from Berge's maximum theorem. If $H$ is locally compact, as it is the case if $H=\mathbb{R}^n$, then such a function can always be found, this ...


10

You're looking at it from a particularly biological point of view. I know nothing of side-blotched lizards, but I can say that evolutionary game theory is often used for equilibrium selection. In games with more than one equilibrium (whether it be Nash or otherwise), evolutionary game theory can allow us to select a particular equilibrium that is a better ...


10

In a Bayesian game, information is incomplete. To cope, players have beliefs about the state of the game. In a sense, each player strategizes as if the game was as he or she believes. So each player operates in his or her own world. And if every player plays a Nash equilibrium in one's own world, that's a Bayesian Nash equilibrium. In a stochastic game, the ...


10

LaTeX with forest The forest package of LaTeX allows you to draw game trees with pretty simple syntax. After copying a pre-set template into the LaTeX preamble, one can build up the game tree using a nested [] syntax, then the program takes care of node placement/spacing/etc. pros: customizability (you can annotate the game tree in any way you want) and ...


10

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 ...


9

Introducing the language of beliefs here is slightly strange, given that beliefs do have a very specific meaning in other parts of game theory. Indeed, Osborne's description is reminiscent of a Bayes Nash Equilibrium. We could introduce the notion of beliefs into the normal form of a complete information game as follows: suppose that with probability $a_i$ ...


9

As you implied, the tragedy of the commons was the standard theory in Economics. This is no longer the case. However--and this is an important point--rejection of this one-size-fits-all approach to public resource management did not come from the emergence of new theories; rather, it resulted from actually studying real-world outcomes. In fact, it's for her ...


9

Iet's say we have n identical firms and an infinite horizon of time. The n firms sustaining the collusion, will find optimal to fix the same price $p_m$ where $p_m$ is the price of the monopoly level and we define $\frac{\Pi^m}{n}$ as the profits each firm is obtaining by sustaining the collusion in each moment t. Now, of course each firm can betray the ...


9

Yes, there is such a setting. The result is that If each player's strategy space is convex compact and if payoffs are continuous then there exists at least one Nash equilibrium (possibly in mixed strategies). This holds even when the set of possible actions is uncountably infinite. If one additionally assumes that payoffs are ...


9

Without the teacher, everyone knows that there is at least a red hat, but nobody knows that everyone knows - the fact is not common knowledge. With the introduction of the teacher, Girl 1 doesn't answer. Due to common knowledge, 2 and 3 can reason: "1 knows there is at least one red hat, and since she doesn't know her hat color, 2 and/or 3 must have a ...


9

The idea is precisely that players do not chose actions, but only chose one action at the time at every node at which they play, based on their beliefs about the way other players and themselves will play at future nodes in the game (where beliefs are conditional on the history that led to that node). The interpretation is letting players choose full-...


9

Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January. I disagree with your assertion that EGT ...


9

I believe that the answer given by @denesp is incorrect. The second method involves simply writing the game in strategic of "normal" form. I believe the first method is better (easier to use), but I think that they can both be used. In the answer given by @desesp, the following explanation is given. The reason why method two is flawed is that the ...


9

Yes, there is no equilibrium in pure strategies. For any price charged by firm 2 above $c_1$, firm one could only best respond by charging the largest price that is strictly smaller. which is impossible. If both firms charge at most $c_1$, one of these firms must make a loss, which cannot be a best response. So there is no Nash equilibrium in pure strategies....


9

What he's saying is that once the burger is already made, the cost of making the burger is a sunk cost, and thus the marginal cost of the burger is just the cost of the tiny labor involved in picking it up and selling it to the customer. That's sort of an odd position to take. Obviously once the burger is cooked you can't recuperate the costs, but in the ...


9

If you think that the distribution of your value and your roommate's value are the same then I would suggest that you consider the following bidding protocol: each bidder submits a sealed bid, $b_i$. the highest bidder, $i$, received the console and makes a payment of $\frac{b_i+b_j}{2}$ to the loser, where $b_j$ is the loser's bid. Cramton, Gibbons, and ...


9

Not really. There are many compact metrizable topologies you can put on this space, but none that relate meaningfully to the structure of the problem. Let's look first at the case $A_1=[0,1]$ and $A_2=\{0,1\}$. Consider the elevation function $e:A_1\times\Sigma\to\Delta(A_2)=[0,1]$ given by $e(a,\eta)=\eta(a)$. If you want the ultimate action choice of ...


8

You might want to be a little more precise about what you mean by "Revelation Principle" as there are many formulations of the "Revelation Principle" out there, some of which are stronger than others. Each of these formulations makes a different claim and relies on a particular set of assumptions. Of course, the claim will often fail to be true if some of ...


8

The problem you are facing has probably both: Moral Hazard and Adverse Selection. We have hidden action by the doctor (you can't really observe his level of effort during the surgery), therefore we have Moral Hazard. Additionally, you (probably) can not know beforehand of the doctor is a good or bad doctor, so his type (good or bad) is unknown. So, there ...


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