IF YOU ARE PLANNING TO BUY A USED CAR

Logon to Examine Buy End Start No Yes

HOW TO DECIDE: IT COULD BE A LEMON Earlier people would take it to a mechanic for a careful examination

OVERVIEW The model Characterizing optimal strategies for the searcher the expert Market design

SEQUENTIAL MODEL The Searcher Noisy signal Reject & Start again Buy & Terminate

THE MODEL Expert and Searcher: Rational Agents Expert sets profit maximizing fee Searcher formulates utility maximizing strategy Stackelberg game

8 STACKELBERG GAMES Model One player (leader) has dominate influence over another Typically there are two stages One player moves first Then the other follows in the second stage Can be generalized to have multiple groups of players Static games in both stages Main Theme Leader plays by backwards induction, based on the anticipated behavior of his/her follower.

NOTATION

DISTRIBUTIONS fv(x) fs(y|v) fv(y|s) fs(x)

OVERVIEW The model Characterizing optimal strategies for the searcher the expert Market design

IF HAVING NO EXPERT… … but rather just noisy signals: S – signals for which we buy

HSGN

MAIN CLAIM The proof is based on showing that, if according to the optimal search strategy the searcher should resume her search given a signal s, then she must necessarily also do so given any other signal s’ < s Use V to denote the expected value of continuing the search

MAIN CLAIM (CONT.) If better to resume search given s: Given HSGN: Therefore: Now: Optimize according to t to get part (a) of the theorem

NOW WITH THE EXPERT… General Strategies: Reject some (without consulting the expert) Accept some (without consulting the expert) Consult the expert and then decide if to reject or accept

THEOREM Claim – given HSGN, the optimal strategy for the searcher is based on (tl,tu,v)

PROOF First show that if, optimally, the searcher should resume her search given a signal s, then she must also do so given any signal s’ < s If the optimal strategy given signal s is to resume search then the following two inequalities hold:

PROOF (2) And similarly, if better to terminate for s then so is for s’>s Based on HSGN

BOTTOM LINE

EXPERT’S PROFIT

CALCULATING the expected overall number of queries made

AN EXAMPLE s

Reject Accept Query & decide

EFFECT OF c e AND d e

OVERVIEW The model Characterizing optimal strategies the searcher the expert Market design

SOCIAL WELFARE Social welfare = Searcher’s Utility + Expert’s profit Expert’s Profit : Searcher’s Utility :

MARKET DESIGN Does it make sense for market designer to subsidize the query cost of an expert

MARKET DESIGN

CLAIM The optimal level of subsidy for an additive measure of social utility is the level that forces the buyer to exactly fully internalize the cost of provision of expert services