class: center, middle, inverse, title-slide # 3.5 — Using Game Theory in Research ## ECON 316 • Game Theory • Fall 2021 ### Ryan Safner<br> Assistant Professor of Economics <br> <a href="mailto:safner@hood.edu"><i class="fa fa-paper-plane fa-fw"></i>safner@hood.edu</a> <br> <a href="https://github.com/ryansafner/gameF21"><i class="fa fa-github fa-fw"></i>ryansafner/gameF21</a><br> <a href="https://gameF21.classes.ryansafner.com"> <i class="fa fa-globe fa-fw"></i>gameF21.classes.ryansafner.com</a><br> --- # Game Theory .pull-left[ .smallest[ - Game theory appears somewhat tautological - Result of game is baked into the rules of a game specified - Game theorists often know the result even before the players play - More useful as a **theoretical framework** for understanding strategic interactions - If players were rational and had perfect information — what would they do? - Compare the (theory) prediction with reality - Do players act differently in reality? ] ] .pull-right[ .center[  ] ] --- # When Results are Not as Predicted .pull-left[ - Behavioral economists: - Did players make a mistake? Act less than "rational"? - Cognitive biases, behavioral economics explanations - Did players not understand the rules? - Game theorists: - Did you specify the game correctly? - Are the rules correctly modeled? - Are the payoffs correctly specified? ] .pull-right[ .center[  ] ] --- # Research with Game Theory .pull-left[ .smallest[ - Most fruitful part of research (in my biased opinion) is using game theory to understand the role of *institutions* (norms, culture, shared histories, government policies, etc.) - Coordination devices - Focal points - Sorting between multiple Nash equilibria - Path dependent outcomes - Making threats/promises credible - Making exchanges self-enforcing - Resolving asymmetric information problems - We'll see this starting this week, and in the papers we'll read ] ] .pull-right[ .center[  ] ] --- # The Two Major Models of Economics as a “Science” .pull-left[ ## Optimization - Agents have .hi[objectives] they value - Agents face .hi[constraints] - Make .hi[tradeoffs] to maximize objectives within constraints .center[  ] ] -- .pull-right[ ## Equilibrium - Agents .hi[compete] with others over **scarce** resources - Agents .hi[adjust] behaviors based on prices - .hi[Stable outcomes] when adjustments stop .center[  ] ] --- # Game Theory vs. Decision Theory Models I .pull-left[ .center[  ] ] .pull-right[ - Traditional economic models are often called .hi[“Decision theory”]: - .hi-purple[Optimization models] **ignore all other agents** and just focus on how can **you** maximize **your** objective within **your** constraints - Consumers max utility; firms max profit, etc. - **Outcome**: .hi-purple[optimum]: decision where *you* have no better alternatives ] --- # Game Theory vs. Decision Theory Models I .pull-left[ .center[  ] ] .pull-right[ - Traditional economic models are often called .hi[“Decision theory”]: - .hi-purple[Equilibrium models] assume that there are **so many agents** that **no agent’s decision can affect the outcome** - Firms are price-takers or the *only* buyer or seller - **Ignores all other agents’ decisions**! - **Outcome**: .hi-purple[equilibrium]: where *nobody* has any better alternative ] --- # Game Theory vs. Decision Theory Models III .pull-left[ .center[  ] ] .pull-right[ - .hi[Game theory models] directly confront .hi-purple[strategic interactions] between players - How each player would optimally respond to a strategy chosen by other player(s) - Lead to a stable outcome where everyone has considered and chosen mutual best responses - **Outcome**: .hi-purple[Nash equilibrium]: where *nobody* has a better strategy **given the strategies everyone else is playing** ] --- # Equilibrium in Games .pull-left[ .center[  ] ] .pull-right[ - .hi-purple[Nash Equilibrium]: - no player wants to change their strategy **given all other players’ strategies** - each player is playing a **best response** against other players’ strategies ] --- # A Suggested Framework .pull-left[ I. Identify the strategic interaction - Who are the players - What choices can they make? - How does the *interaction* of their choices determine outcomes for each player? ] .pull-right[ .center[  ] ] --- # A Suggested Framework .pull-left[ .smallest[ II. Model the game: rules, payoffs, etc (*often the hard part!*) - Ordering of choices -- sequential, simultaneous? - Information -- what does each player know and not know - One-shot or repeated? - If repeated: a finite number of times? an infinite number of times? ending with certain probability? - Define the payoffs (*again, the hard part*!) - use *economic theory* to determine how various interactions should affect various outcomes for each player - numerical payoffs make things easy, but constrain you to fewer possibilities - using *variables* in payoffs allows you to solve for the *conditions* that will yield *different Nash equilibria* ] ] .pull-right[ .center[  ] ] --- # A Suggested Framework .pull-left[ III. Predict the outcome(s) - Solve for Nash equilibria - If applicable, consider: pure vs. mixed strategies, one-shot vs. repeated games - If using variables in payoffs, what values of variables will give us various equilibria? - If multiple equilibria -- any reasons we should expect one over others? ] .pull-right[ .center[  ] ] --- # A Suggested Framework .pull-left[ .smallest[ IV. Compare reality with predictions - Are there behavioral reasons players do not reach predicted outcome? - Are there institutions, policies, norms, ethics, etc. that lead players towards/away from certain outcomes? V. Consider changes in the game - What would have to change (payoffs, rules, etc) to get different outcomes? - Are there policies or institutions that might affect or cause this? - Consider welfare of players: how do the players do? How could this be improved? ] ] .pull-right[ .center[  ] ] --- class: inverse, center, middle # Example I: Patronage, Copyright, and Crowdfunding as Alternative Institutions --- # Patronage .center[  ] --- # Patronage Today .center[  ] --- # Patronage Today .center[  ] --- # Patronage Today .center[  ] --- # Basic Game .pull-left[ .smallest[ - .red[Creator] can produce a (single) expressive work - Fixed cost `\(F\)` - Marginal cost `\(C\)` - If produced, incur cost `\(-(F+C)\)`, and sell at price `\(P\)` - .blue[Consumer] can consume or copy expressive work - Values it at `\(V\)` - Purchases at price `\(P\)` - `\(V-P\)`: consumer surplus - Copies with replication cost, `\(R\)` ] .source[Safner, Ryan, 2021, “Kickstart My Art: Are Crowdfunding and Intellectual Property Complements or Substitutes?”] ] .pull-right[ .center[  ] ] --- # Basic Game .pull-left[ - Solve this game by backwards induction: - Consumer will Purchase when: - `\(R>P\)`: costlier to copy than to purchase - `\(V>P\)`: price to buy is lower than value (i.e. consumer surplus, `\(V-P \geq 0\)`) - Producer will Produce when: - Consumer Purchases - `\(P>F-C\)`: revenue exceeds cost .source[Safner, Ryan, 2021, “Kickstart My Art: Are Crowdfunding and Intellectual Property Complements or Substitutes?”] ] .pull-right[ .center[  ] ] --- # Mechanisms to Enhance Cooperation .pull-left[ .smallest[ - An agent ("patron") bears the fixed costs (F) in exchange for some of the following: - Distribution rights (copyrights); personal prestige; portion of profits; rewards - Deterrence of pirating & shirking (raise R relative to P) - Technology affects replication costs; Customization, product differentiation, price discrimination; Legal threats; Reputation - Compare three systems: 1. Patronage of the arts 2. Copyright 3. Crowdfunding ] .source[Safner, Ryan, 2021, “Kickstart My Art: Are Crowdfunding and Intellectual Property Complements or Substitutes?”] ] .pull-right[ .center[  ] ] --- # Patronage of the Arts (& Sciences) .pull-left[ .center[  ] ] .pull-right[ .center[  ] ] --- # Patronage Version of the Game .pull-left[ .smallest[ - .hi-purple[Patronage of the arts]: institution that changes the rules of the game - .blue[Consumer-Patron] decides to sponsor a .red[Creator] by bearing their fixed costs F - .red[Creator] now in a principal-agent problem: produce or shirk (abscond with F) - Rules of the game that affect key parameters: - Removes opportunity of copying (custom works) - F: fixed costs now borne by .blue[patron] ] .source[Safner, Ryan, 2021, “Kickstart My Art: Are Crowdfunding and Intellectual Property Complements or Substitutes?”] ] .pull-right[ .center[  ] ] --- # Copyright .pull-left[ - Cost of replication has plummeted via new technology (both for creators & for copyists) - Copyright: Individual creator can control distribution rights and seek legal sanctions against copyists .source[Safner, Ryan, 2021, “Kickstart My Art: Are Crowdfunding and Intellectual Property Complements or Substitutes?”] ] .pull-right[ .center[   ] ] --- # Copyright Version of the Game .pull-left[ - .hi-purple[Copyright]: another institution that changes the *payoffs* of the original game - If .blue[Consumer] chooses to Copy, now faces additional: - `\(D\)`: damages from copyright lawsuit - `\(\sigma\)`: probability of getting caught/sued - .red[Creator] gains `\(\sigma D\)` (from lawsuit against .blue[Consumer]), but must pay `\(E\)` for enforcement costs (legal fees) .source[Safner, Ryan, 2021, “Kickstart My Art: Are Crowdfunding and Intellectual Property Complements or Substitutes?”] ] .pull-right[ .center[  ] ] --- # Copyright Version of the Game .pull-left[ - .blue[Consumer] purchases when: - `\(P<R-\sigma D\)` - More likely than first version of game .source[Safner, Ryan, 2021, “Kickstart My Art: Are Crowdfunding and Intellectual Property Complements or Substitutes?”] ] .pull-right[ .center[  ] ] --- # Patronage with Copyright/Crowdfunding Version .pull-left[ - .hi-purple[Patronage with Copyright]: *three* players - patron and consumer are different - patron can sponsor creator by bearing `\(F\)` - patron contracts for copyright and some share `\(\alpha\)` of the profits - .hi-purple[Crowdfunding]: patrons `\(\neq\)` wealthy elites, but a collection of many people contributing towards `\(F\)` .source[Safner, Ryan, 2021, “Kickstart My Art: Are Crowdfunding and Intellectual Property Complements or Substitutes?”] ] .pull-right[ .center[  ] ] --- # Example II: 19^th Century American Literary Piracy .pull-left[ - From 18^th—mid 20^th century the United States *refused* to respect copyright of *foreign* authors - American publishing industry expressly built on piracy of foreign works (mostly British novels) - The U.S. is now the world's copyright policeman, enforcing its copyrights internationally .source[Safner, Ryan, 2021, “Pirate Thy Neighbor: The Protectionist Roots of International Copyright Recognition in the United States” Safner, Ryan, 2021, “Honor Among Thieves: How 19th Century American Pirate Publishers Simulated Copyright Protection”] ] .pull-right[ .center[  ] ] --- # Example II: 19^th Century American Literary Piracy .pull-left[ .smallest[ - U.S. publishers' piracy of foreign authors in the 19^th century faced a tragedy of the commons: - No exclusive claims over printing foreign works (no copyright `\(\implies\)` no right to exclude) - Solved this problem by creating a publishing cartel that created "property rights" in piracy of foreign authors - Enabled protectionist resistance to calls for respecting international copyrights - System broke down by end of 19^th century - Rising U.S. cultural output in 20^th century: publishers now advocate for international copyrights ] .source[Safner, Ryan, 2021, “Pirate Thy Neighbor: The Protectionist Roots of International Copyright Recognition in the United States” Safner, Ryan, 2021, “Honor Among Thieves: How 19th Century American Pirate Publishers Simulated Copyright Protection”] ] .pull-right[ .center[  ] ] --- # Game Setup .pull-left[ - Two representative American publishers, 1 and 2; two authors `\(A\)`, and `\(B\)` - Publisher 1 moves first and decides to publish `\(A\)` or `\(B\)` at profit-maximizing price `\(p\)` with cost `\(c\)` - Publisher 2 moves second and can decide to publish: - the *same* author as 1 ("pirate") at lower cost `\(\hat{p}<p; \hat{c}<c\)` or - the *other* author at cost `\(c\)` .source[Safner, Ryan, 2021, “Pirate Thy Neighbor: The Protectionist Roots of International Copyright Recognition in the United States” ] ] .pull-right[ .center[  ] ] --- # Game Setup .pull-left[ - Consumers will buy only from lower-priced publisher - If publisher 2 pirates, can sell at lower price than publisher 1 - If both publish different authors, each earns `\(p_i-c\)`, where `\(i=\{A, B\}\)` - Authors `\(A\)` and `\(B\)` may fetch different prices `\(p_A\)` and `\(p_B\)` depending on market demand .source[Safner, Ryan, 2021, “Pirate Thy Neighbor: The Protectionist Roots of International Copyright Recognition in the United States” ] ] .pull-right[ .center[  ] ] --- # Game Setup .pull-left[ - Piracy/original publishing depends on: - relative value of author `\(A\)` vs `\(B\)` - profits of original sales `\((p_i-c)\)` vs. profits of pirate sales `\((\hat{p_i}-\hat{c})\)` - both demand for pirated works `\((\hat{p_i})\)` and reproduction technology `\((\hat{c})\)` .source[Safner, Ryan, 2021, “Pirate Thy Neighbor: The Protectionist Roots of International Copyright Recognition in the United States” ] ] .pull-right[ .center[  ] ] --- # Game Outcome - Role of Institutions .pull-left[ - Parameters `\(p_A\)`, `\(p_B\)`, `\(c\)`, and `\(\hat{c}\)` are determined by market conditions and institutions: - Historically, several methods to secure property rights and deter piracy from other publishers - Arts patronage - Monopoly/guild (Stationers' Company of London) - Internal trade organizations - Copyright law .source[Safner, Ryan, 2021, “Pirate Thy Neighbor: The Protectionist Roots of International Copyright Recognition in the United States”] ] .pull-right[ .center[  ] ] --- # The Cartel Solution: “Courtesy of the Trade” .pull-left[ .smaller[ - 1790—1891 U.S. did not recognize copyrights to foreign authors - U.S. publishing industry largely pirated famous British authors - Set up “courtesy of the trade” system of voluntary norms to avoid tragedy of commons - Created pseudo-property rights in foreign authors works - Ended up paying authors despite no obligation to, nor any legal protection earned ] .source[Safner, Ryan, 2021, “Pirate Thy Neighbor: The Protectionist Roots of International Copyright Recognition in the United States” Safner, Ryan, 2021, “Honor Among Thieves: How 19th Century American Pirate Publishers Simulated Copyright Protection”] ] .pull-right[ .center[  ] ] --- # The Cartel Solution: “Courtesy of the Trade” .pull-left[ .smallest[ - 1790—1891 U.S. did not recognize copyrights to foreign authors - Resolved the tragedy of the commons problem via a cartel - A publisher would announce which foreign author they would publish and stake their "claim" - Other publishers would refrain from republishing that author, in hopes that when they stake a claim on a different author, others would respect it - If didn't respect claims, retaliation: nobody would respect their future claims ] .source[Safner, Ryan, 2021, “Pirate Thy Neighbor: The Protectionist Roots of International Copyright Recognition in the United States” Safner, Ryan, 2021, “Honor Among Thieves: How 19th Century American Pirate Publishers Simulated Copyright Protection”] ] .pull-right[ .center[  ] ] --- # More General Solutions .pull-left[ - 1891 International Copyright Act “respects” foreign copyrights in U.S. - “Manufacturing clause” required foreign works to be printed in U.S. - Rationale for “trade courtesy” cartel disappears - U.S. publishers begin publishing U.S. authors - Now in their interest to push for other countries to respect U.S. copyright .source[Safner, Ryan, 2021, “Pirate Thy Neighbor: The Protectionist Roots of International Copyright Recognition in the United States”] ] .pull-right[ .center[  ] ]