ECON 522 - SECTION 3-DYNAMIC GAMES AND INTELLECTUAL PROPERTYI Dynamic GamesDynamic games are just like static games, except players move sequentially rather than simulta-neously. The definition of Nash equilibrium is still the same (everyone is playing a best response),but now we can end up with NE that don’t make a lot of sense. In the example from class, a startup firm has to choose “enter” or “do not enter,” and the incumbent firm must choose to “fight”or “accommodate.” However, we end up with a strange NE in which the new firm chooses notto enter and the incumbent chooses fight, even though the first firm should figure that a rationalincumbent firm would never actually fight should the first firm enter the market. Thus we intro-duced the idea of sequential rationality: everyone believes everyone will behave rationally at everypoint in time. This leads to a “refinement” of Nash equilibrium, which we call subgame perfectequilibrium (SPE), which is just a NE in which everyone is behaving sequentially rationally. Wesolve these games using backwards induction, which just means we start from the end of the gameand see what choices people would make if they ever reach those end situations, and we workour way back up to the beginning. You can use this method to solve a lot of strategic interactivegames, such as tic-tac-toe, or checkers.I.1 Back to a static game- the Public Goods Game from classSetup: There are 100 people with identical preferences represented by: u = 10√X − x, where Xis the total amount of money (including what that individual contributes) donated for a publicpark, and x is the amount donated by the individual. Note that just like in the tragedy of thecommons example, we can break up the total payment X into how much you pay, x, and howmuch everyone else pays, X − x = X. Now we can solve our maximization problem by taking thederivative of our utility and setting it to zero:u = 10√X − x = 10pX + x − x⇒u0= 10 ×12(X + x)−12− 1 = 0⇒5 = (X + x)12⇒25 = X + xRemember from the tragedy of the commons example that we can guess that since everyonehas the same utility, then all of the individuals in this society will choose to contribute the sameamount, so X = 99x ⇒ 25 = 99x + x ⇒ x = $0.25. The point is that this is not efficient.If everyone contributes $0.25, then each individual’s utility will only be: u = 10√25 − .25 =49.75, but they would get more everyone donated $1 instead (check this). In fact, if we werethe benevolent government, we could optimally tax people and provide the public good. Thegovernment knows that individuals are the same, so it can set X = 100x and maximize society’sutility:u = 10√X − x = 10√100x − x = 100√x − x⇒u0= 100 ×12(x)−12− 1 = 01⇒50 = x12⇒2500 = xSo the optimal (efficient) amount for each person to donate is $2500! That’s a lot more than $0.25(Check to make sure that people actually have higher utility if they are taxed $2500 a piece toprovide the public good). This is an example of how the government can increase efficiency byproviding public goods. The reason that public goods are underfunded is that individuals don’tinternalize the fact that they’re imposing positive externalities on others when they help supplythe public good. This is exactly analogous to the tragedy of the commons example, except inthat example individuals weren’t internalizing negative externalities, thus the result was too muchfishing. Another thing to note about this (the public good) example, is that the more people thereare in the society, the less each individual wants to donate; it’s easier to free ride when there aremore people.II Intellectual Property• Private Goods are rivalrous (my use prevents your use) and excludable (I can prevent youruse)– Usually it’s more efficient for private goods to be privately owned. However, some-times this may not be true. Take our example of smoker’s rights. As far as Coase isconcerned, assigning the right to smoke to smokers or non-smokers will result in an ef-ficient allocation as long as people can negotiate. The right to smoke-free/smoke-filledair is rivalrous and potentially excludable, but trade may be impossible due to hightransaction costs. Thus it may be more efficient for the government to regulate, anddesign what it believes to be efficient smoking rules.• Public Goods are nonrivalrous (my use does not prevent your use) and nonexcludable (I cannotprevent your use)– Usually it’s more efficient for public goods to be publicly owned. However, sometimesthis my not be true. Intellectual property often fits the categories of non-rivalrous andnon-excludable (once an idea has been created it’s hard to stop someone from using it,and certainly one person’s use doesn’t preclude another’s).Let’s explore the differences between public/private goods some more, and see why intellectualproperty gives us problems.First notice that a good being rivalrous does not imply that it’s also excludable, or vice versa.Likewise, non-rivalrous does not imply non-excludable. An example of a good thats rivalrous andnon-excludable (so that it doesn’t fall into either the public/private good category) is the fish inthe tragedy of the commons example.Next notice that intellectual property fits the description of a public good, so we should think thatit’s efficient to for it to be publicly owned/funded, and in fact a lot of it is: right now as studentsat a public university you are at least partially being funded by the government, and there aremany other examples of government funding research and development. However, it may alsobe efficient to own intellectual property privately, in which case we would need to at least attemptto make it excludable and rivalrous. This is where our four types of intellectual property come in:2(i) Patents-property rights over novel, non-obvious, sellable inventions; last 20 years and mustbe applied for.(ii) Copyrights-property rights for original expression; last 70 years after creator’s death andare automatically given upon creation of the expression.(iii) Trademarks-Last until they’re abandoned (which is why companies must actively defendtheir trademarks, much like a land owner must establish use of the land to prevent squat-ters).(iv) Trade secrets-Protect secrets from being obtained illegally.Intellectual propertyType Economic RationalePatent To align private incentives with social benefit/cost;
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