H6: Bargaining and auctions theory
Introduction
Surplus splitting in economics
=> So far: studied firms competing on the market, benefits from trade (surplus) were
- Producer selling above their costs (profits)
- Consumer buying for less than their WTP (consumer surplus)
- Prices determined who and how much surplus was generated
=> However, many contracts are formed or adjusted outside the market
- Split of profits in collusion agreements
- Employee negotiating for a raise
- Allocation of resources within the firms/teams
=> In this part, we take a more general look at negotiations different from price
setting, and how surplus is allocated
- When surplus is known: bargaining (with complete information)
- Competitive bargaining: model the bargaining as game => most used
- Cooperative bargaining: study desirable solutions to bargaining
problems
- When surplus is unknown: Auctions
- And “screening” => Lec 6 and lec 7
- Bargaining is under asymmetric information exists, it is very complex
and often reduced to screening or auction problems to make it tractable
Bargaining theory
Bargaining in general
- Studies situation where stipulating a deal is efficient (there is a surplus)
- But, conditional on agreement, the game is strictly competitive: for an agent to
gain something, another player needs to lose something
- A common example are zero-sum (finite-sum)-games: the payoff of one
player is equal to the loss of the other
Determinants of bargaining outcomes
1) Psychological factors
- Anchoring bias, overconfidence… (behavioural economics)
- Non-verbal communication (posturing, voice techniques…)
2) Sociological factors
- Power & social structures
- Social identity & in-group effects
3) Economic and strategic factors (this lecture)
- Ultimatum and commitment
- Outside options
- Agents patience
- Information
1
, Our goal is to understand how these factors affect:
- Who gains what share of the surplus
- What constitutes an advantage in the game
- When and how an agreement is reached
=> See outcome our bargaining game on slides
Ultimatum game: SPNE
=> Solve by using backward induction
- Stage 2: Receiver's decision
=> for any 𝛼, the receiver is choosing between 𝛼V and 0
=> accept for any 𝛼>=0
- Stage 1: Dealer’s decision
=> Since the receiver accepts any arbitrarily small offer, the dealer maximizes
their payoff choosing the smallest possible offer: 0
=> SPNE <(𝛼 = 0, A(𝛼) = “Accept” for 𝛼 >= 0 )> (strategy function)
- This is an extreme result: all the bargaining power is in the hand of the dealer
=> What if we let the receiver make a (final) counter offer
2
Introduction
Surplus splitting in economics
=> So far: studied firms competing on the market, benefits from trade (surplus) were
- Producer selling above their costs (profits)
- Consumer buying for less than their WTP (consumer surplus)
- Prices determined who and how much surplus was generated
=> However, many contracts are formed or adjusted outside the market
- Split of profits in collusion agreements
- Employee negotiating for a raise
- Allocation of resources within the firms/teams
=> In this part, we take a more general look at negotiations different from price
setting, and how surplus is allocated
- When surplus is known: bargaining (with complete information)
- Competitive bargaining: model the bargaining as game => most used
- Cooperative bargaining: study desirable solutions to bargaining
problems
- When surplus is unknown: Auctions
- And “screening” => Lec 6 and lec 7
- Bargaining is under asymmetric information exists, it is very complex
and often reduced to screening or auction problems to make it tractable
Bargaining theory
Bargaining in general
- Studies situation where stipulating a deal is efficient (there is a surplus)
- But, conditional on agreement, the game is strictly competitive: for an agent to
gain something, another player needs to lose something
- A common example are zero-sum (finite-sum)-games: the payoff of one
player is equal to the loss of the other
Determinants of bargaining outcomes
1) Psychological factors
- Anchoring bias, overconfidence… (behavioural economics)
- Non-verbal communication (posturing, voice techniques…)
2) Sociological factors
- Power & social structures
- Social identity & in-group effects
3) Economic and strategic factors (this lecture)
- Ultimatum and commitment
- Outside options
- Agents patience
- Information
1
, Our goal is to understand how these factors affect:
- Who gains what share of the surplus
- What constitutes an advantage in the game
- When and how an agreement is reached
=> See outcome our bargaining game on slides
Ultimatum game: SPNE
=> Solve by using backward induction
- Stage 2: Receiver's decision
=> for any 𝛼, the receiver is choosing between 𝛼V and 0
=> accept for any 𝛼>=0
- Stage 1: Dealer’s decision
=> Since the receiver accepts any arbitrarily small offer, the dealer maximizes
their payoff choosing the smallest possible offer: 0
=> SPNE <(𝛼 = 0, A(𝛼) = “Accept” for 𝛼 >= 0 )> (strategy function)
- This is an extreme result: all the bargaining power is in the hand of the dealer
=> What if we let the receiver make a (final) counter offer
2
