Strategic Interaction: Game Theory PDF

Strategic Interaction: Game Theory Class 2 Fall 2024 Block 2 Economics for Political Science Leiden University 1  Today Social dilemmas, incentives and strategic interaction Col...

Strategic Interaction: Game Theory Class 2 Fall 2024 Block 2 Economics for Political Science Leiden University 1  Today Social dilemmas, incentives and strategic interaction Collective action among self-interested actors with poor trust Games as analytical devices for situational awareness & strategy Identifying incentives (payoffs) and dominant strategies Single and multiple stable outcomes (equilibria) Invisible hand, prisoner’s dilemma, and coordination games Enhanced cooperation strategies: Iterated games (repeated interaction Institutions with monitoring and enforcement Side-payments to improve outcomes for all (bridge to class 3) 2 Social Dilemmas, Strategic Interaction Economic (and political) actors do not act in isolation We have to deal with other people  Our actions impact others & the action of others impact us Even coordination can be hard when we want to This produces opportunity (gains) and conflict (losses) For individuals, groups, and also countries (so IR) Game theory provides a framework to understand these interactions We choose second-best even when we want to be good to avoid others hurting us 3  Social dilemmas: negative outcomes, despite incentives to cooperate Actions taken independently by self-interested individuals result in a socially suboptimal outcome e.g. traffic jams, climate change. Three kinds:  Social dilemma 1: public goods Public goods are non-excludable Once they are supplied, anyone can consume for free Non-rival goods: consuming the good does not reduce supply for others Utilities, lighthouses, as examples Prone to free riding: Benefiting from the contributions of others without contributing oneself Solution is typically public provision and payment (taxes) Since incentives inhibit cooperation  Social dilemma 2: Tragedy of the commons: Common-pool resources: Resources are shared by a group Sustainability requires restraint from all group members Free riding is the key problem: If you reduce your carbon footprint, reduce pollution or limit the number of tuna you catch, you will bear the costs Others who don’t will enjoy the benefits, until the resource is entirely depleted  Social dilemma 3: joint goods Joint goods: private goods enjoyed by actors only if they can cooperate In companies, management and employees need each other Cooperate or fight over share of company income, working hours & conditions Distribution of cooperation benefits is main problem Power struggles over distribution common  Game Theory: Core Concepts Game theory is an analytical tool and method (not a theory) Assumes individuals are rational and act strategically: Why don’t actors always reach agreements? Which outcomes are more probable? Developed in 1970s (Google: ”John Nash, Beautiful Mind”) 8  Game Theory: Core Concepts Social interaction: Each actor’s behaviour affects everyone’s outcomes Strategic interaction: Each actor is aware of how their behaviour affects everyone’s outcomes May involve communication or not Strategy: Actions taken that consider the outcomes and likely behaviour of others. Best choice considering others’ actions may be different than first choice in a perfect world. 9  Elements of a Game A game describes a social interaction: 1. Players – who is involved in the interaction 2. Feasible strategies – actions each player can take 3. Information – what each player knows when choosing their action 4. Payoffs – outcomes for every possible combination of actions Example: Rock-Paper-Scissors 10  Game types Invisible hand: actors maximise benefits without any real strategy Describes specialization for win-win outcomes in free trade situations Prisoner’s Dilemma: introduces negative consequences for cooperation actors experience pressure to not cooperate, even though benefits are high Assumes no communication. Coordination: actors choose strategy closest to preferences given constraints of what another actor does, poor information on intent Tragedy of the Commons: Cooperation without government? 11 The Invisible hand Two farmers decide which crop to specialize in. They interact only once (one-shot game). 1. Players – Anil and Bala 2. Feasible strategies – Rice or Cassava 3. Information – each farmer does not know what the other chooses 4. Payoffs – depend on market prices and quality of land 12  Invisible hand payoff matrix Payoff matrix = A table of the payoffs associated with every possible combination of strategies chosen by two or more players in a game 13  Best response We can use the payoff matrix to analyze what action a player would choose if s/he knew what the other player will do. Best response: Strategy that will give a player the highest payoff, given the strategies that the other players select. If Bala chooses Rice, Anil’s best response is to choose Cassava— that gives him 4, rather than 1. 14  Dominant strategies Dominant strategy: Action that yields the highest payoff for a player, no matter what the other player does. Anil’s payoffs are highest by growing Cassava, regardless what Bala does – this is his dominant strategy. Note that a dominant strategy need not always exist! 15  A dominant strategy equilibrium Dominant strategy equilibrium: An outcome of a game in which every player plays his or her dominant strategy Equilibrium (in general): Self-perpetuating situation. A state or outcome that does not change unless outside forces a change When Anil and Bala each play their dominant strategy, the outcome is (Cassava, Rice). 16  The invisible hand The pursuit of self-interest can lead to outcomes that are socially desirable. If circumstances are right. Requires complementary self-interests coupled with specialization Choosing the strategy that generates the highest personal payoff—resulted in an equilibrium: Each player got the best of the four possible outcomes/payoffs (everyone’s a winner) Total payoffs combined higher (society is a winner) Note: application in benefits of trade 17  Problems with the Invisible Hand Sometimes following your self interest can lead to: Sub-optimal outcomes (underperformance) Really bad outcomes (e.g. climate change) Negative externalities (bad outcomes for others) What if there are downsides to what others do? How does strategic interaction change? 18 The prisoner’s dilemma: Incentives undermining cooperation 19  Two criminals are caught. There is not enough evidence to convict them of entire crime. The government offers both the same deal Snitch on the other and get off free If both snitch you get 5-years If you remain silent you get 20 years if your partner snitches If both remain silent, light 1-year sentence What would you do? 20  Collectively, both would do better by cooperating (staying silent) (lower right) Yet, each has an incentive to defect (or snitch on) his accomplice In this diagram “confess” Defection is the best response to avoid high costs given incentives and uncertainty of what the other will do (upper left) 21 22  Prisoner’s Dilemma Lessons Individual incentives often make cooperation difficult Selfish behavior can lead to suboptimal outcomes Simple model with strong implications for economics and social behavior: Used in IR theory: to cooperate with a strategic rival or not? Is coordination still possible? 23  Coordination Game: Pesticides & Sustainability Two farmers decide how to deal with pest insects: organic or pesticides? 1. Players – Anil and Bala 2. Feasible strategies – Terminator or Integrated Pest Control (IPC) 3. Information – Each farmer does not know what the other chooses 4. Payoffs – Depend on the resulting combination of pest control instruments 24  Equilibrium in the pesticide game Given weak cooperation expectations, (Terminator, Terminator) is the dominant strategy equilibrium. Both farmers choose this. (2/2 payoff) Both farmers would be better off collectively using IPC instead. But with weak commitments, neither does. 25  Tragedy of the Commons Tragedy of the Commons concerns common property goods. Goods are rival in consumption and non-excludable (to the group) unchecked behavior leads to over-exploitation Not everything on the earth is easily owned Water Air Public lands Markets tend to work well and resources preserved when individuals own property and have an incentive to maintain and preserve it. 26  Tragedy of the Commons Several cow-herders live near a common area used for grazing Common resources, but rival incentives Each can maintain the existing livestock or add an additional cow to add profit Individual short-term incentives ahead of collective long-term incentives (sustainability) Additional cows lead to overgrazing and underfed cows >> everyone loses Garett Hardin, 1968 27  Tragedy of the Commons Elinor Ostrom (Political Scientist with a Nobel Economics Prize for her solution): Farmers can create rules & transparency to support credible commitments Requires good information & willingness to exclude or sanction the defector People on the spot better at decisions than bureaucrats or politicians 28  Nash equilibria as most likely outcomes In many other games, players do not have Crop game with different payoffs dominant strategies: each player’s strategy is a best response to the strategies chosen by everyone else. For example, your best response of which side to drive will depend on what the others choose to do. Nash equilibrium: a set of strategies, one for each player in the game, such that each player’s strategy is a best response to the strategies chosen by everyone else. Actors avoid other choices, leading to outcomes In this new crop game, there are two Nash equilibria! Because the payoffs are different. Context of payoffs matters 29  Conflicts over which equilibrium will occur There may be mutual gains to getting to one or the other of these equilibria, but who gets the lion’s share of these gains may differ among the outcomes. Example: Two software engineers both do better if they work in the same language. Astrid does better if the language is Java, while the reverse is true for Bettina. Two Nash equilibria: both choose Java or both choose C++. The outcome might be determined by: - Which of the two has more power? - Who started work on the project first? 30  Conflicts over climate protection efforts The worst outcome for both countries is that both persist with BAU, running a significant risk of human extinction. The best for each is to continue with BAU and let the other one Restrict. The only way to moderate climate change significantly is for both to Restrict.  Conflicts over climate protection efforts There are two Nash equilibria: Actors differ on which country bears the cost of restricting emissions. As long as costs are bearable. These two Nash equilibria are such that the two players adopt different strategies. Negotiations are bound to be difficult, since each country would prefer the other to take the lead on restricting carbon emissions. The game represents the idea that no one wants to see catastrophic climate change, but neither wants to lose to the other and adjust first, or adjust more.  Joint goods & striking workers Strikes or lockouts as failed cooperation= (lost income for workers and company) Reduces GDP (sometimes in the broader economy) Wage coordination mechanisms can help avoid but not eliminate conflict Businesses and unions may hate the idea of cooperating with ‘the enemy and fight. Coordination designed to promote negotiation in good faith Similar to environmental restriction game 33 Joint goods example: Boeing workers striking Strikes hurt workers & company Union Cooperates Union Fights (-4/-4) Cooperation (fair wages) best for both, (4/4) Company 4/4 2/6 Cooperat es Company could win concessions to serve shareholders, not workers (6/2) Company 6/2 -4/-4 Fights Union could win concessions to serve workers, not shareholders (2/6) 34 Joint goods example: Boeing workers striking 35  Bargaining to resolve problems When we confront these problems in economics, political science, or international relations bargaining outcomes are solved through Hard bargaining Availability of alternatives decreases need to accept unattractive terms BATNA: Best Alternative To a Negotiated Agreement Sometimes a skewed Nash equilibrium outcome 36  Bargaining to resolve problems What if bargaining includes mechanisms to extend bargaining results into the future? Creating a credible commitment (institutions & enforcement)) This can support the ideal compromise scenario Or enforce a one-sided negotiation outcome Examples: Wage coordination mechanisms and tribunals Trade agreements, institutions and dispute settlement mechanisms 37  Repeated games We have so far looked at one-shot games. Better outcomes can arise in repeated interactions due to social norms, reciprocity, and peer punishment. Behaving selfishly in one period has consequences in future periods, so it may no longer be a dominant strategy. Copycat behaviour works best: Cooperate, but punish defections and return to nice (tit for tat) Listen (recommended): Planet Money podcast “Nice Game” 38  Try out your best cooperation strategy! https://ncase.me/trust/ 39  Toolkit to overcome social dilemmas Repeated interaction: Collective payoffs increase through long-term cooperation Selective punishments against cheaters can correct behaviour (tit-for- tat retaliation) Fewer number of players: It is easier for cooperation to emerge when there are few actors In collective action problems to cost of individual defection are high It is easier to monitor defection in repeated interaction 40  Toolkit to overcome social dilemmas Monitoring, enforcement and institutions (“See you in court”!) To set guidelines or rules, monitor compliance and & strengthen commitments Everyone gets confirmation that others follow the rules Also to sort out enforcement & adjudication (dispute resolution) Social norms and persuasion (“See you soon”!) Norms of fairness, appropriateness of actor behaviour 41  Psychological Bias & Game Theory Gaps People don’t meet high standards of perfectly rationality Imperfect information & cognition (ability to process costs/benefits rationally) and biases: Loss aversion – hold value of potential losses high than equal potential gains (compulsive gamblers, not losing face or status) Discounting behavior – care less about future gains/losses/threats (see climate change, government debt, what your vote will mean) Behavioral Economics is dedicated to impact of psychology on strategic choice. 42  Psychological Bias & Game Theory Gaps Social preferences: some people care what happens to others. Even at personal cost. Especially during catastrophes Altruism – benefiting others for greater good, social norms Inequality aversion – preference for equal outcome 43  Takeaways 1. Social dilemmas are sub-optimal outcomes in the absence of government Pursuing self-interest (without malice) can lead to socially beneficial or undesirable outcomes (not malice) Cooperation without government is the main challenge 2. Game theory helps us model strategic interactions Social interactions: actors seek gains, but may conflict over distributing payoffs Based on incentives and absence of trust Invisible hand, prisoner’s dilemma, coordination problems (pesticides & strikes) Players choose best responses to others’ strategies Nash equilibria can still cause coordination problems, incite hard bargaining Leading to hard bargaining, importance of BATNA  Next Class We will explore public policy options for improving collective action & overall output Preferences and policies to address social dilemmas Including market failure Institutions, public provision and tax policy as unique mechanisms Improving on outcomes with credible commitments and side-payments Read the section on Pareto Optimization closely. 45