L8 - Game Theory: Bargaining I Flashcards
What is Bargaining?
- Some contemporary Examples
- Brexit negotiations over a UK-EU trade deal and ongoing bargaining over Northern Ireland Protocol
- Climate Change global discussions
Why study bargaining?
- Explain, predicts and improve key activity in our world
- Useful building block for other areas of economics:
- Industrial economics, political economy, labour economics, environmental economics, financial economics
- Relevant for much of our own lives and careers
What is cooperative game theory?
- non-cooperative game theory –> where players select strategies to maximise their individual payoffs. –> equilibria/equilibriums
- In contrast, cooperative game theory implicitly allows players to enforce binding agreements, perhaps through an arbitrator. This can enable players to obtain outcomes that would not form part of an equilibrium under noncooperative game theory.
- For example, within cooperative game theory, players could sign a contract to enforce an outcome where both players cooperate in a prisoners’ dilemma in order to maximise joint payoffs.
- Of course, more modern non-cooperative game theory would disallow such binding agreements and instead require any prediction to be immune from individual profitable deviations
- For the topic of bargaining, both approaches have their merits and it is common to study both.
- The cooperative approach makes use of an axiomatic analysis by asking what properties we would expect a bargaining solution to exhibit. This is very different approach to our usual equilibrium way of thinking
- The non-cooperative approach places more structure on the specific bargaining context to analyse individual behaviours and intereaction
How to set up a Cooperative Game?
What does the Bargaining set look like including monetary transfers?
- Can transfer the other player all of their ‘utility’ as a monetary payoff
- the net Surplus is the value added by coorperating
What is the Solution to the cooperative approach game?
- Nash (1950) suggested a unique solution to such bargaining problems using an axiomatic approach.
- Under an axiomatic approach, a researcher makes use of a list of characteristics that they think any reasonable outcome ought to exhibit.
- (With binding agreements) it is reasonable to expect the solution to have the following two properties:
- Efficient - it maximises joint value, UA + UB = V*
- Individually rational - each player has a payoff that is at least as large as their disagreement payoff; Ui ≥ di for all players
What are the three further properties a unique solution to a bargaining problem should exhibit?
Nash also suggested the solution should exhibit three other properties:
- Symmetry – the solution should be symmetric if the players are identical. Any asymmetry in the solution should be generated only from differences in the players’ utility functions or disagreement points.
- Invariance – the solution should not depend on how the utility is measured.
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Independence of Irrelevant Alternatives (IIA) – if an outcome is removed that does not include the existing solution, U* , or the disagreement vector, d, then U* should remain as the solution.
* Blue share shows the areas which is maximised by the Nash Product
Summary of how to find a Nash bargaining Solution?
QUESTION!
Two housemates, Jodi and Rani, both want some beer from the local shop. Jodi is trying to persuade Rani to make the journey on their behalf to save her going.
If Rani agrees, Jodi gains a utility of 120 and Rani gains a utility of 60. However, if Rani does not go, they both gain a utility of 10.
Calculate how much Jodi will pay Rani to go using the Nash bargaining solution.
What happens if we have asymmetric disagreement payoffs in a cooperative bargaining game?
- Player A gets a boost in their utility and pays less in the monetary transfer
- the new disagreement payoff shifts the nash bargaining solution to the right
Application of cooperative bargaining to real-world situations notes?
NOTE:
Necessary components:
- • Understand the theory
- • Understand the real-world situation
- • Try to blend the two to give a theoretically informed perspective and insight.
Don’t just give an intelligent analysis of the situation without using the theory.
Try to analyse the real-world situation through the lens of the theory using the language and apparatus of the model. Often the theory won’t fit perfectly.
Be aware of this, adapt, but be cautious in what the theory can and can’t say.
In this past BBC article about Brexit negotiations, here, it says:
“If a trade deal is not agreed, the UK will trade with the bloc on World Trade Organisation rules - leading to tariffs being introduced on many imports and exports, which could push up costs for businesses and consumers.
Both sides say they want to avoid this outcome, but the EU has said it will not do a deal “at any price”, and Mr Johnson has said the UK will prosper either way.”
Try to interpret this statement in the light of bargaining theory. How can we understand the two parties’ statements?
- theory assumes we know the disagreement vector/payoff for both parties –> however this assumption is not true –> EU didn’t know the UK assessment of what they believed the payoffs were and vice versa
- What would happen if we don’t agree on Brexit –> Boris says we will be fine but will we even though we don’t want the WHO trade guidelines
- EU and UK estimate what they believe is going on and use their statements to influence the other person view of the disagreement vector
- UK trying to tell EU that we will find even if we disagree (influence dA and in turn their total final utility)
How can we evaluation Nash’s bargaining solution?
The Nash bargaining solution is interesting, useful, and relatively easy to use but
- • In many situations, binding agreements are unrealistic
- Make sense to us but is that how people will behave (are they actually rational (behavioural economics))
- • Axiomatic approach may be misleading – how agents ‘ought’ to behave is not necessarily how agents actually do behave.
- • The actual bargaining process is a black box
To help address these limitations, we will study the non-cooperative approach in the next lecture
