11 Game Theory and River Sharing Flashcards
Game Theory Basics
• Powerful technique for analyzing behavior in case actions of individuals are
interdependent and decisions of others are not known in advance
• Applied in presence of global or regional public goods, and externalities
spilling over national boundaries
Two-player binary choice game
see table on # lecture 11 slide 203
- Net benefit pay off
- First number net benefits player A
- Second number net benefits player B
- Abatement cost per unit 7 for one country
- Benefit ( per unit abatement 5 to each country
Dominant strategy and Nash equilibrium
- A dominant strategy is a strategy that has a higher pay off than any other, irrespective of the choice made by other players
- “A set of strategic choices is a Nash equilibrium if each player is doing the best possible given what the other is doing”
Dominant strategy and Nash equilibrium
Results (1)
- Solution is a Nash equilibrium
- State of environment is worse than it could be
- Outcome is Pareto inefficient in case they both abate each would gain a net benefit of 3
- Pay off matrix is an example of the so called prisoner’s dilemma
- Incentives do not support abatement of pollution
- There is a single Nash equilibrium that results from both players following their dominant strategy
- Many environmental problems could be described by the Prisoner’s dilemma
Dominant strategy and Nash equilibrium
Results (2)
- Cooperative outcome would be better
- [abata, abate] is not a Nash equilibrium!
- Each has an incentive to defect from an agreement → free riding
- Cooperative solution is an unstable solution
- Binding agreement possible?
- Penalty clauses e g pay 3.5 units if you defect → new payoff matrix
- Solution is not realistic
- There must be a third party to monitor and enforce agreement
- In a world of sovereign states, no enforcer exists
• Agreement between nations must be self enforcing in order to sustain
A two-player “Chicken” game (1)
• Same structure as the previous game
• Change: if both countries
pollute, each will incur a damage of 4 (benefit of 4)
• What happens?
A two-player “Chicken” game (2)
- Same structure as the previous game
- Change: played sequentially
• We can solve by backward
induction
• What happens?
Note: First move advantage!
A two-player “Assurance” game
• Cost of contribution 8
• Benefits enjoyed by two
countries only of both
contribute 12
• Two Nash Equilibria
• In a repeated game, a self
enforcing mechanism can be reached
Note: In a repeated game, if player A keeps contributing for whatever reason, eventually player B will also contribute to get a pay-off
What’s the point?
- Agents (in our case the users of water) face choices about their treatment of water
- The interaction with different agents add a strategic component
- By adding game theory, we can predict outcomes of those situations
- We have seen situations in which cooperation would increase everyone’s welfare
Grand Coalition: Different Flow of the Stream
• River flows can differ seasonally, annually, or be interfered with by human action
• For instance, the construction of hydropower dams in China’s Yunnan region affects Mekong
downstream users
- The same issue currently affects relations between Egypt and Ethiopia due to the Grand Ethiopian Renaissance Dam
- What are some of the possible impacts on the flow of the river?
Coalitions and Negotiations
• What is supposed to happen in case efficient allocation is not achieved?
- Negotiations between agents
- Forming of coalitions or sub coalitions
- Agreement on compensation payments and acceptability conditions of transfers (core issue in cooperative game theory)
- Defining what a group can achieve by itself, and what the value of cooperation would be
- How much water will flow depends on the behavior of sub groups
