Lobbying and Corruption Dr James Tremewan (james.tremewan@univie.ac.at) Lobbying As Strategic Information Transmission
Lobbying As Strategic Information Transmission • In the Tullock model it was assumed that lobbying expenditure increased the probability of a desired outcome, but the precise mechanism was not specified. • A lot of lobbying involves informing policy makers of ”private” information, e.g. a firm’s costs, scientific information on the environmental impact of pollutants, health impact of drugs, wage expectations of union members etc. • Often lobbyists have an incentive to misinform, or withhold information. • Policymakers are aware of lobbyist’s interests. • Game of ”strategic information transmission”: Under what circumstances can lobbyists credibly transmit information to a policymaker and be believed? 2/17
Model 1 • Two players: government ( G ) and interest group ( F ). • Government must select an action x ∈ { x 1 , x 2 } • Payoffs depend on ”state of the world” variable θ ∈ { θ 1 , θ 2 } : G,F θ = θ 1 θ = θ 2 x = x 1 a 1 , 0 0 , 0 x = x 2 0 , b 1 a 2 , b 2 • Only F knows the value of θ . G has prior belief that θ = θ 2 with probability p . • F has the option of sending a message m to G at cost c ( m ) = c , or no message ( n ) which is costless ( c ( n ) = 0). • We can assume the message is ” θ = θ 2 ” (although the content of the message doesn’t actually matter). 1 Lobbying and asymmetric information , Jan Potters and Frans van Winden, Public Choice (1992) 3/17
Equilibrium (in words) • Equilibrium strategies will often be ”mixed”, i.e. probabilities a certain action will be taken. • A Lobbying Equilibrium consists of: • (1) probability F sends a message for each value of θ . • (2) probability G chooses x 2 if F does/does not send message. • (3) set of ”reasonable” beliefs that G has about the probability that θ = θ 2 depending on whether message is sent. • An equilibrium requires that: • (1) F maximises utility given G ’s strategy. • (2) G maximises utility given beliefs about θ , and F ’s strategy. • (3) G updates beliefs using Bayes’ rule and the actual probabilities from F’s strategy if possible. If one of F ’s actions is never taken in equilibrium, G should believe the state of the world is the one where F is ”most likely” to send that signal. • (1), (2) like for Nash equilibrium. (3) means G ’s beliefs correct in equilibrium (beliefs should change if systematically wrong). 4/17
Equilibrium (in algebra) • Further notation: • σ ( s ) is the probability G chooses x = x 2 after receiving signal s ∈ { m , n } ). • ρ i ( s ) for i ∈ { 1 , 2 } is the probability F sends message s when θ = θ i . • q ( s ) is G ’s posterior (subjective) probability that θ = θ 2 after observing signal s . • A Lobbying Equilibrium is pair of strategies σ, ρ such that: • (1) if for some s i ∈ S , ρ i ( s ) > 0 then s maximizes b i σ ( s ) − c ( s ); in addition � S ρ i ( s ) = 1 for i = 1 , 2, • (2) if σ ( s ) > 0( < 1) for some s ∈ S , then q ( s ) ≥ ( ≤ ) α = a 1 / ( a 1 + a 2 ), • (3) q ( s ) = p ρ 2 ( s ) / [(1 − p ) ρ 1 ( s ) + p ρ 2 ( s )] if the denominator is positive; if not, the belief q ( s ) must be concentrated on the type F i which is ’most likely’ to send the off-equilibrium signal s . 5/17
Equilibria • Equilibria depend on precise parameter values. • We will now discuss the intuition behind equilibria in a few different cases (for formal proofs and other cases, see paper). • In all three cases we will assume p < a 1 / ( a 1 + a 2 ). This condition means that if G is not given more information they will choose x = x 1 . • We will also assume b 1 , b 2 > 0. 6/17
Equilibrium ( b 1 > b 2 > 0) G,F θ = θ 1 θ = θ 2 x = x 1 a 1 , 0 0 , 0 x = x 2 0 , b 1 a 2 , b 2 • If b 1 > b 2 > 0, no message will be believed, so no lobbying occurs. • ρ 1 ( m ) = 0, ρ 2 ( m ) = 0, • σ ( n ) = 0, σ ( m ) = 0, • q ( n ) = p and q ( m ) = 0. • F only wants to reveal information if θ = θ 2 . • But F has a larger stake in convincing G if θ = θ 1 (i.e. more likely to accept cost of message), so if G gets a message they will think θ = θ 1 . 7/17
Equilibrium ( c > b 2 > b 1 > 0) G,F θ = θ 1 θ = θ 2 x = x 1 a 1 , 0 0 , 0 x = x 2 0 , b 1 a 2 , b 2 • If c > b 2 > b 1 > 0, no lobbying occurs: • ρ 1 ( m ) = 0, ρ 2 ( m ) = 0, • σ ( n ) = 0, σ ( m ) = 1, • q ( n ) = p and q ( m ) = 1. • The cost of sending a message is greater than the maximum F can gain from convincing G that θ = θ 2 . • Note that we have to specify off-equilibrium actions and beliefs to fully define equilibrium. • A message is never sent in equilibrium, so we can’t use Bayes’ rule to update beliefs after m . F is ’more likely’ to send message when θ = θ 2 ( b 2 > b 1 ), so if G observes m they believe θ = θ 2 . • This means they must choose x 2 after observing m for their strategy to be utility maximising. 8/17
Equilibrium ( b 2 > c > b 1 > 0) G,F θ = θ 1 θ = θ 2 x = x 1 a 1 , 0 0 , 0 x = x 2 0 , b 1 a 2 , b 2 • If b 2 > c > b 1 > 0: • F sends a message only if θ = θ 2 ( ρ 1 ( m ) = 0, ρ 2 ( m ) = 1). • G chooses x 2 if they receive a message, and x 1 otherwise ( σ ( n ) = 0, σ ( m ) = 1). • q ( n ) = 0 and q ( m ) = 1. • If θ = θ 1 then sending a message costs more than their maximum possible benefit, so if a message is sent then G knows θ = θ 2 . 9/17
Equilibrium ( b 2 > b 1 > c > 0) G,F θ = θ 1 θ = θ 2 x = x 1 a 1 , 0 0 , 0 x = x 2 0 , b 1 a 2 , b 2 • If b 2 > b 1 > c > 0: • ρ 1 = p (1 − α ) / [(1 − p ) α ], ρ 2 = 1, • σ ( n ) = 0, σ ( m ) = c / b 1 , • q ( n ) = 0 and q ( m ) = α . • α = a 1 / ( a 1 + a 2 ) 10/17
Check equilibrium conditions ( b 2 > b 1 > c > 0) • F ’s strategy: • Check that if θ = θ 2 , F is at least as well off sending message as not, given G’s strategy . • Check that if θ = θ 1 , F is indifferent between sending message and not, given G’s strategy (always with mixed strategies, the player must be indifferent between the actions they are mixing over, otherwise they would choose the better option for sure). • G ’s strategy: • Check that G is at least as well off choosing x 1 as x 2 , given equilibrium beliefs after receiving no message . • Check that G is indifferent between x 1 as x 2 , given equilibrium beliefs after receiving a message . • Beliefs: Check that G ’s beliefs satisfy Bayes’ rule after both receiving and not receiving a message. 11/17
Overview • Whether or not effective lobbying take place depends on: • Incentive’s of F at least partially in line with G ′ s (i.e. b 2 > b 1 ). • The cost of lobbying: • Costs too high, F can never afford to lobby. • Medium costs, lobbying is affordable and can influence G . • If lobbying free, ignored by G (remember σ ( m ) = c / b 1 ). Only costly messages can credibly communicate information. • Expected payoffs: Expected Payoffs G F No lobbying (1 − p ) a 1 0 b 2 > c > b 1 > 0 (1 − p ) a 1 + pa 2 pb 2 − c b 2 > b 1 > c > 0 (1 − p ) a 1 pc ( b 2 / b 1 − 1) • Efficiency: lobbying increases efficiency in equilibrium; most efficient when F able to transmit private information perfectly ( b 2 > c > b 1 > 0). 12/17
Potters and van Winden (2000) 2 • The experiment in this paper implements in the laboratory two games like those we have just seen. • Some sessions run with students, some with professionals (public affairs and public relations officers from private and public sectors). • Both students and professionals paid about their hourly wage (4 times as much for professionals). • Main questions: • Does the theory predict subject behaviour? • Do students behave differently from professionals? 2 Professionals and students in a lobbying experiment: Professional rules of conduct and subject surrogacy, Jan Potters and Frans van Winden, Journal of Economic Behavior and Organization (2000). 13/17
Experimental Games • Changes in notation: • ”Sender” has private information about state of world: White (p=2/3) or Black (p=1/3) (disk chosen from urn). • ”Responder” chooses B 1 or B 2. • Low message cost (c=0.5): R,S Black White B 1 3 , 2 0 , 1 B 2 1 , 4 1 , 7 • High message cost (c=1.5): R,S White Black B 1 3 , 1 . 5 0 , 1 . 5 B 2 1 , 3 . 5 1 , 5 . 5 • Equilibria: • Low cost: ρ w = 1 4 , ρ b = 1, σ ( n ) = 0, σ ( m ) = 1 4 . • High cost: ρ w = 1 4 , ρ b = 1, σ ( n ) = 0, σ ( m ) = 3 4 . • Responder more likely to choose B2 after m with high cost. 14/17
Results 15/17
Results • Supporting the theory: • Costly messages are sent and receiving a message makes it more likely B 2 is chosen. • Messages are more often sent when Black. • More costly messages are more influential. • Against the theory: • Precise proportions for all decisions are quite far from equilibrium predictions. • Messages sent too often (little) when White (Black). • B 2 chosen too much after no message (and too little after message in high cost treatment). • Messages sent less in high than low cost treatment when White. • Professionals play closer to equilibrium predictions when Sender : • More successful at transmitting useful information, and earn more than students. 16/17
Recommend
More recommend
