The Local Government’s Subsidy Game in Cultural

｢지방정부연구｣  제12권 제1호(2008 봄) : 351～363

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Technology Industry Policies*

* This work was supported by 2005 Overseas Research Grant of LG Yonam Foundation.

** I would like to thank Eric Rasmusen for the helpful suggestions provided on earlier drafts.

문화산업정책에서 나타나는 지방정부의 보조금 게임

Shin, Hee-Guon**

최근 우리나라에서는 선진국에서와 마찬가지로 지방정부들이 문화산업을 전략산업으로 육성하려는 정책적 노력들을 보여주고 있다. 그러나 낮은 성과와 문화산업 업체들의 지대추구(rent-seeking)에 대한 비판이 적지 않은 바, 본 연구에서는 보조금을 둘러싼 지방정부와 문화산업 업체간의 상호작용을 분석하기 위해 3개의 수리적(數理的) 보조금게임 모형을 살펴보고 있다. 이 모형을 살펴본 결과, 주인-대리인 이론에서 나오는 여러 정책적 함의, 예를 들어 역(逆)선택, 도덕적 해이, 계약이후의 감춰진 지식, 교차 검증 등이 지방정부의 문화산업정책 보조금에도 거의 그대로 적용됨을 알 수 있었다. 또한 계약이후의 감춰진 지식에 의해 문화산업 업체의 정보 지대가 오히려 감소하고, 교차 검증이 지방정부와 문화산업 업체가 상대방에게 진실된 메시지를 보내게 만드는 균형을 보장한다는 것을 알 수 있었다.

주제어 : 문화산업정책, 보조금게임, 주인-대리인

Ⅰ. Introduction

Nowadays many local governments in Korea, such as Busan, Gwangju, Daejeon, Bucheon and so on, try to invigorate cultural technology industries with diverse policy tools as other local governments did in the developed countries. Cultural technology(CT) industries are becoming more important in "knowledge-based economies" - economies which are directly based on the production, distribution and use of knowledge and information. Knowledge or content, as embodied in human capital and in technology, has always been central to economic development. But only over the last decade has its relative importance been recognized in Korea, just as that importance is growing. As one of the representative industries in knowledge-based economies, CT industries also rest on the premise that understanding the linkages among the actors involved in innovation is the key to improving technology performance. The innovative performance of CT industries depends to a large extent on how these actors relate to each other as elements of a collective system of knowledge creation and usage as well as the technologies they use (Im, 2004). These actors are primarily private businesses, universities and public research institutes. The linkages can take the form of joint research, personnel exchanges, cross-patenting, purchase of equipment and a variety of other channels (Bilton & Leary, 2002). What is important is the web of interaction or the system, and many local governments want to induce this system by their policy tools.

In a 2006 survey (Ministry of Culture and Tourism, 2006a), astounding 33.7 % of the principal CT businesses in Daejeon said they "need more financial support". 21.2 % of those surveyed said they "need more facilities/equipment support" and another 21.2 % said they "need more marketing support". They thought support for personnel recruitment(5.8 %), technology consulting(3.8 %), management consulting(2.9 %), education/training academy(1.0 %) and so forth respectively. So we can see that Local Government's subsidy is very important as a CT industry policy tool.

The Local Government’s Subsidy Game in Cultural Technology Industry Policies

｢지방정부연구｣ 제12권 제1호(2008 봄)

Ⅱ. Cultural Technology Industry

Cultural contents loaded on informational technology(IT) infrastructure are critical to cultural technology(CT) industries: movies, game, animation, character, broadcasting, music and so forth. CT industries have been characterized by the words, "environment-friendly", "knowledge-based" and "highly value-added". Also "one source, multi use" window effects and increasing returns to scale make CT industries more attractive. In 2005 year the total sales in Korean CT industries recorded 53,948 billion Won, and showed the annual growth rate of 7.8 % which is much greater than the GDP's growth rate of 4.2 % (Ministry of Culture and Tourism, 2006b: 23). Especially the annual growth rate of game industry skyrocketed to 101.1 %. The annual growth rate of broadcasting industry was 11.1 % and that of movies industry was 9.0 %. So we can see that game, broadcasting and movies industries are growing much faster than the other CT industries in Korea. In 2005 year the total sales of the CT industries in Korea reached to 6.65 % of the GDP and 2.38 % of the GDP contribution ratio. Comparing with the fact that the average rate of CT industries' contribution to the GDP is 6-7 % in the USA, Japan and so on, we can conclude that the potential growth rate of CT industries in Korea would be very high.

CT industry policies, however, are often criticized for the low outcome and intrinsic rent seeking behaviors. So it would be profitable to analyze the game between the local government and CT business on the subsidy to CT industries.

<Figure 1> CT industries based on IT

The economics and finance literatures have developed theoretical models that analyze the optimal contract between the shareholders and the manager of a firm. In the traditional framework, as developed in the seminal paper by Holmstrom(1979), the underlying problem is that the shareholder(principal) cannot observe, and therefore cannot contract upon, actions taken by the manager(agent) that affect profitability even though the consequences of these actions ultimately affect the shareholders' returns. The action, which provides disutility for the agent, together with a random state of nature determines the observable profit of the firm. The issue in contract design is to provide the agent with the incentive to take the action. A risk-neutral principal could, of course, eliminate the incentive problem by making the agent the residual claimant of the profit, but the agent is risk-averse and so shifting the risk to her entails an efficiency cost. The optimal contract, therefore, reflects a trade-off between the incentive benefit of conditioning the agent's compensation on the observed level of profit and the cost of inefficiency allocating the risk to the risk-averse party.

But in the local government's cultural technology(CT) subsidy game, the agent is not a person but an organization(CT business, university, research institute). So the agent would be not risk-averse but risk-neutral. From this, we can make a new principal-agent model, "MODEL 1".

Levin(2003), also, makes a general treatment of relational contracts between risk-neutral parties with asymmetric information, moral hazard and hidden information.

Ⅲ. MODEL 1

What will happen to the game when adverse selection and moral hazard are interconnected, so that cultural technology businesses face the game with private information but then also take unobserved actions in the course of the local government’s subsidy game?

In CT industries' innovation system, as mentioned earlier, principal actors are primarily private businesses, universities and public research institutes. And they all would become a counterpart player of Local Government in subsidy game. If then, they all would have similar payoffs respectively. So we will use a CT business as a representative counterpart player in analyzing Local Government's subsidy game.

In moral hazard problems combined with hidden knowledge, the contract need to ordinarily satisfy only one participation constraint, whereas in adverse selection problems a different participation constraint for each type of cultural technology businesses is required. An exception is if there are constraints limiting how much a cultural technology business can be punished in different states of the world. For example, if there are bankruptcy constraints, then if the cultural technology business has different wealths across the N possible states of the world, there will be N constraints for how negative his subsidy can be, in addition to the single participation constraint. These can be looked at as interim participation constraints, since they represent the idea that the cultural technology business wants to get out of the contract once he observes the state of the world midway through the game.

PLAYERS

Local Government (the principal) and a cultural technology business (the agent)

THE ORDER OF PLAY

0  Nature picks the state of the world s, which can be observed by a cultural technology business while but not observed by Local Government, according to distribution F(s), where the good state occurs with probability 0.5 and the bad state with probability 0.5.

1  Local Government offers the cultural technology business a subsidy contract c(q).

2  The cultural technology business accepts or rejects the contract.

3  The cultural technology business chooses subsidy-relevant effort level e.

4  Subsidy-relevant output is q = q(e,s), where q(e,good) = 3e and q(e,bad) = e.

PAYOFFS

If the cultural technology business does reject all contracts, then we will have πbusiness = Ū and πgovernment = 0.

Otherwise, we will end up with πbusiness = U(e,c,s) = Ū+c-e2 and πgovernment = V(q-c) = q-c.

Thus, no uncertainty is involved, both Local Government and cultural technology business are risk-neutral in money, and subsidy-relevant effort is increasingly costly.

In this model, the first-best effort depends on which the state of the world we are given. If the Social Planner rules the world, his two social surplus optimization problems will be like the followings.

Maximize (Ū+3eg-eg2),        Maximize (Ū+eb-eb2)

eg                            eb

From those two optimizations, we can derive that in the good state, the optimal subsidy-relevant effort is eg = 3/2 (and qg = 9/2), and in the bad state, the optimal subsidy-relevant effort eg = 1/2 (and qg = 1/2). However, the problem is that the Local government does not know what level of subsidy-relevant effort and output are just right for the problem. Local government does not want to impose high output on the cultural technology business in both states. If Local government does, Local government will have to allot too high a subsidy to the cultural technology business as compensation for the difficulty of obtaining that output in the bad state.

Thus, Local Government must solve the problem

Maximize [0.5(qg-cg)+0.5(qb-cb)]	(1)

qg,cg,qb,cb

where the cultural technology business has to choose between two forcing contracts, (qg,cg) and (qb,cb), and the contracts must include controls for participation and self-selection behaviors.

The self-selection constraints are derived from subsidy-relevant efforts of e = q/3 for the good state and e = q for the bad state. In the good state, the cultural technology business must select the good-state contract, so

πbusiness(qg,cg|good) = Ū+cg-(qg/3)2 ≥ πbusiness(qb,cb|good) = Ū+cb-(qb/3)2	(2)

and in the bad state the cultural technology business must choose the bad-state contract, so

πbusiness(qb,cb|bad) = Ū+cb-qb2 ≥ πbusiness(qg,cg|bad) = Ū+cg-qg2.	(3)

The participation constraints are

πbusiness(qg,cg|good) = Ū+cg-(qg/3)2 ≥ Ū

and

πbusiness(qb,cb|bad) = Ū+cb-qb2 ≥ Ū.    ==>    cb = qb2

The participation constraint in the good state will not be binding, since there the cultural technology business will be left with an informational rent - Local Government must leave the cultural technology business some surplus as a mechanism design to induce it to reveal the good state.

The self-selection constraint in the good state will be binding, since in the good state the cultural technology business will be exposed to the temptation to accept the easier contract appropriate for the bad state. Thus, we can obtain conclusion from constraint (2) that

cg = (qg/3)2+cb-(qb/3)2,

= (qg/3)2+ qb2-(qb/3)2,

where the second line substitutes for cb. The self-selection constraint in the bad state will not be binding, since the cultural technology business would then not be tempted to produce a large amount for a large subsidy.

Now let's discuss the Local Government's maximization problem again. Having obtained expressions for cb and cg we can rewrite (1) as

Maximize [0.5{qg-(qg/3)2-qb2+(qb/3)2}+0.5(qb-qb2)]

qg,qb

with no constraints. The first-order conditions are

0.5(1-2qg/9) = 0

==>     qg = 4.5

0.5(-2qb+2qb/9)+0.5(1-2qb) = 0

==>     qb ≈ 0.26

The second-order condition for maximization is satisfied, which is obvious and skipped. We can then find the amounts of subsidies that satisfy the constraints, which are cg ≈ 2.32 and cb ≈ 0.07.

Thus, in the second-best world of asymmetric information, the effort in the good state is still the first-best effort, but the second-best effort in the bad state is smaller than the first-best. This results from Local Government’s need to keep the bad-state contract from being too attractive in the good state. Bad-state output and compensation must be suppressed. Good-state output, on the other hand, should be left at the first-best level, since the agent will not be tempted by that contract in the bad state.

Also we can observe that in the good state the cultural technology business earns an informational rent. This is because in the good-state the cultural technology business could always obtain a positive payoff by pretending the state was bad and accepting that contract, so any contract that can distinguish out the good-state cultural technology business (while leaving some contracts acceptable to the bad-state cultural technology business) must also enjoy a positive payoff.

But this standard model ignores a critical feature of the relationship between Local Government and the CT business: the CT business may also possess private information about the true output and may falsify that information in his report to Local Government. Recent experiences suggest that an optimal contract between Local Government and the CT business should be designed not only to provide the CT business with an incentive to take actions that may enhance the actual output, but also to minimize the CT business's incentive to falsify output reports. From this, we can make an another principal-agent model, “MODEL 2”.

Ⅳ. MODEL 2

Information is complete in moral hazard games. What if we are discussing moral hazard with hidden knowledge (in other word, postcontractual adverse selection)? In this situation, only the CT business (but not Local Government) observes a move of Nature right after the beginning of the game but before the CT business takes its action. The information in this game is symmetric at the time of making contract (thus simply the "moral hazard") but becomes asymmetric later (thus the "hidden knowledge").

From the Local Government's point of view, CT businesses are identical at the beginning of the game but develop private types in some point of the game and maintain those through. Local Government's main interest is to design exact incentive mechanism for them to disclose their types later, which gives the game a flavor very similar to that of adverse selection. The CT business might also have to pour effort in the game, but contractibility about effort is less significant when Local Government does not know which effort is appropriate because he is fully ignorant of the state of the world that Nature provides to the game. The main difference is that if information is symmetric at the starting point and only becomes asymmetric after a contract is signed, the participation constraint is based on the CT business's expected payoffs across the different types of CT business it might become. Thus, there is just one participation constraint even if there are eventually N possible types of CT businesses in the model, rather than the N participation constraints that would be required in a standard adverse selection model.

<Figure 2> Sequence of Events

|

<-------------------  | -------------------->

Symmetric uncertainty  | CT business has private

about s         | information about s

|

|

1                 2                3                 4                5

------------------------------------------------------------------------------------------------------> time

Local Government's offer about subsidy contract	CT business accepts or rejects the offer	Nature chooses the state s, CT business observes s, but Local Government does not (Hidden Knowledge)	CT business chooses effort e and message m	Contract implemented, and subsidy is given

What allows postcontractual hidden knowledge to be an ideal setting for the paradigm of mechanism design is that the issue is to construct a contract that (1) induces the CT business to report truthfully to Local Government, and (2) is acceptable to both Local Government and CT business. But one noticeable thing is that there is more hope in postcontractual hidden knowledge for obtaining efficient outcomes than in adverse selection. The advantage is the existence of information to extract surplus from the other by choosing inefficient contract terms.

For a comparison between the two types of moral hazard, let us modify "MODEL 1" and turn it into a slightly different game of hidden knowledge.

PLAYERS

Local Government (the principal) and a cultural technology business (the agent)

THE ORDER OF PLAY

1   Local Government offers the CT business a subsidy contract of the form c(q,m),

where q is output and m is a message to be sent by the CT business.

2   The CT business accepts or rejects Local Government's offer.

3   Nature chooses the state of the world s, according to probability distribution F(s),

where the state s is Good with probability 0.5 and Bad with probability 0.5. The CT

business observes s, but Local Government does not.

4   If the CT business accepted, he exerts effort e unobserved by Local Government, and

sends message m ∈ {good, bad} to Local Government.

5.  Output is q(e,s) where q(e,good) = 3e and q(e,bad) = e, and the subsidy is given.

PAYOFFS

If the CT business rejects the contract, πbusiness = Ū and πgovernment = 0.

If the CT business accepts the contract, πbusiness = U(e,c,s) = Ū+c-e2 and

πgovernment = V(q-c) = q-c.

This game is almost the same as "MODEL 1". The big difference is that now the CT business does not know its type at the point in time at which it must accept or reject the contract. This can be fairly interpreted as the case in which the CT business cannot locate its relative status in the business world. A smaller difference is that we have added the message m which the CT business delivers to Local Government. This message is really 'cheap talk' - it does not make changes on payoffs directly and there is no punishment for lying. It is really useful as a modeling convenience, to indicate which output-subsidy combination the CT business chooses.

Local Government would like to know s so Local Government can tell which effort level is appropriate. In an ideal world Local Government would select an honest CT business who always chooses m = s, but in noncooperative games we ordinarily assume that CT businesses have no moral sense at all. Since the CT business's message is unreliable and worthless, Local Government must try to set up a contract that either provides exact incentive for truth-telling or takes lying into consideration. He designs and implements a mechanism to extract the CT business's information.

In "MODEL 1", the adverse selection version, the optimal contracts had to satisfy two incentive compatibility constraints and two participation constraints.

In "MODEL 2", the moral hazard with hidden information version, the optimal contract must satisfy just one participation constraint, with the same two incentive compatibility constraints.

The first-best solution is the same with "MODEL 1". The optimal effort and output in the good state of the world are eg = 3/2 and qg = 9/2, and in the bad state they are eb = 1/2 and qb = 1/2. Also unchanged is the fact that Local Government must solve the problem:

Maximize [0.5(qg-cg)+0.5(qb-cb)]	(4)

qg,cg,qb,cb

where the CT business is paid under one of two forcing contracts, (qg, cg) if he reports m = good and (qb, cb) if he reports m = bad, where producing the wrong output for a given contract results in boiling in oil.

The contracts must be able to induce participation and self-selection from the CT business. The constraints in terms of the CT business's payoff function from choosing one of the two (q, c) contracts can be rewritten by his choice of the report good or bad. The effort it will choose under those contracts will be e = q/3 for the good state and e = q for the bad state, the same as in "MODEL 1". In the good state, the CT business must choose the good-state, so

πbusiness(qg,cg|good) = Ū+cg-(qg/3)2 ≥ πbusiness(qb,cb|good) = Ū+cb-(qb/3)2	(5)

and in the bad state it must choose the bad-state contract, so

πbusiness(qb,cb|bad) = Ū+cb-qb2 ≥ πbusiness(qg,cg|bad) = Ū+cg-qg2.	(6)

The participation constraints in "MODEL 1" now become one, though, because at the time of contracting the CT business does not know what the state will be. The single participation constraint is therefore

0.5πbusiness(qg,cg|good) + 0.5πbusiness(qb,cb|bad) = 0.5｛Ū+cg-(qg/3)2｝+0.5(Ū+cb-qb2) ≥ 0.

This single participation constraint is binding, since Local Government wants to give the CT business as little as possible. The self-selection constraint in the good state will be also binding. In the good state the CT business will be tempted to take the easier contract appropriate for the bad state (due to the "single-crossing property") and so Local Government has to increase the CT business's payoff from the good-state contract to yield itself at least as much as in the bad state. Local Government wants to increase the surplus up to no more than necessary, though, so the good state's self-selection constraint will be exactly satisfied. This gives us two equations,

The single-crossing property tells that the indifference curves of the two CT businesses do not cross more than once.

0.5｛Ū+cg-(qg/3)2｝+0.5(Ū+cb-qb2) = 0,

Ū+cg-(qg/3)2 = Ū+cb-(qb/3)2

Solving them out yields cb = (5/9)qb2 and cg = (1/9)qg2 + (4/9)qb2.

Returning to the Local Government's maximization problem in (4) and substituting for cb and cg, we can rewrite it as

Maximize πgovernment = [0.5｛qg-(1/9)qg2-(4/9)qb2｝+0.5｛qb-(5/9)qb2｝]

qg,qb

with no constraints. The first-order conditions are

(∂πgovernment)/(∂qg) = 0.5｛1-(2/9)qg｝= 0

==> qg = 4.5

(∂πgovernment)/(∂qb)  = 0.5｛-(8/9)qb｝+0.5｛1-(10/9)qb｝= 0

==> qb = 9/18 = 0.5

We can then find the subsidies that satisfy the constraints, which are cg ≈ 2.36 and cb ≈ 0.14.

As in "MODEL 1", in the good state effort is at the first-best level while in the bad state it is less. Unlike in "MODEL 1" the CT business does not earn informational rents, because at the time of contracting it has no private information. In "MODEL 1" the subsidies were cg ≈ 2.32 and cb ≈ 0.07. Both subsidies are higher in "MODEL 2", but so is the effort and output required of the CT business in the bad state. Local Government in "MODEL 2" is less constrained, and thus able to (1) come closer to the first-best when the state is bad, and (2) reduce the rents to the CT business. Those are general features of moral hazard with hidden knowledge.

Ⅴ. CROSS CHECKING MODEL

Finally, let us move on to the cross checking model. If the state or type is equally revealed to all agents, i.e., public information, then it would be fairly immediate to arrive at the first-best results using forcing contracts. What if the state is observable only to both Local Government and CT business, but is not public information?

In this case, what complicates the problem is that three players are involved in the contracting process: Local Government (the principal) who proposes the contract, the CT business (the agent) who accepts or rejects it - and the citizen jury (the court) that enforces it. If the citizen jury (the court) is excluded from the information about the state, a contract conditioning the subsidy upon the state is unenforceable, no better than having no contract at all. It can be safely said that the variable s is nonverifiable if contracts based on it are not enforceable. Simply enough, the variable would be one whose value the citizen jury (the court) cannot evaluate exactly enough to be useful - a worker's dedication to the job or intensity of effort, for example, as opposed to the number of hours he spent on the job. Or, the variable itself could be something which the citizen jury (the court) would be able to observe but which for some special reasons the citizen jury will not endorse it to be used in a legal dispute or contract - the amount of marijuana in a package, for example.

In this model it is essential to recognize the importances of recruiting the citizen jury upon the context and institutions, and educating citizen jurors. Credible NGOs with merit or specialty need to be the operating host of the citizen jury for improving the effectiveness of cross checking.

It does seem, however, that even though the citizen jury (the court) will not enforce a contract based on a variable if both Local Government and the CT business observe it, they should be able to come up with a more efficient contract than if just the CT business observes it. And indeed, mutual observability can help. Maskin(1999) suggested cross checking, as idea which would take the following two-part form for "MODEL 2":

1 Local Government (the principal) and the CT business (the agent) simultaneously send messages mg and mb to the citizen jury (the court) saying whether the state is good or bad. If mg ≠ mb, then no contract is chosen and both players earn zero payoffs. If mg = mb, the citizen jury (the court) enforces part (2) of the scheme.

2 The CT business is given subsidy (c∣q) with either the good-state forcing contract (2.25∣4.5) or the bad-state forcing contract (0.25∣0.5), depending on its report, mb, or is boiled in oil if the output is inappropriate to its report.

There exists an equilibrium in which both players are willing to send truthful messages, because a deviation would result in zero payoffs. The CT business earns a payoff of zero anyway (the numbers in the forcing contract come from making his participation constraint binding), but that is due to the open-set problem and to our assumption that Local Government has all of the bargaining power. Local Government's payoff is positive and efforts are at the first-best level.

This kind of scheme often has multiple equilibria, however, perverse ones in which both players send false messages and inefficient actions result. Here, in a perverse equilibrium Local Government and CT business would always send the message mg = mb = bad. Even when the state was actually good, the payoffs would be πgovernment(good) = 0.5 - 0.25 > 0 and πbusiness(good) = 0.25 - (0.5)2 = 0, so neither player would have incentive to deviate unilaterally and drive payoffs to zero.

By the way, "mg = mb = good always" could not happen in equilibrium because the CT business would prefer the zero payoff from mismatching to being forced by the threat of boiling oil to try to attain qg when the state is bad.

Ⅵ. CONCLUSION

We made three game-based subsidy models for analyzing the interactions between Local Government and CT businesses. From these models we could find that the principal-agent implications (adverse selection, moral hazard, postcontractual hidden knowledge, and cross checking) are also relevant to Local Government's subsidy game. Also we found the informational rents of the CT business would be reduced via postcontractual hidden knowledge and cross checking would guarantee an equilibrium in which Local Government and a CT business are willing to send truthful messages. These results are meaningful in that they could enlarge the game-based paradigm to Local Government's policy analysis and would contribute to enhance the effectiveness of Local Government's CT industry policies.

This paper terminates only with theoretical prescription without empirical testing. So another empirical analysis about Local Government's subsidy game in Korea would be made in the near future.

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Rasmusen, Eric B. (1993). Lobbying when the Decisionmaker Can Acquire Independent Information. Public Choice, 77: 899-913.

Rasmusen, Eric B. (ed.). (2001). Readings in Games and Information, Oxford: Blackwell Publishing.

신희권(申熙權): 서울대학교 대학원에서 행정학 박사학위를 취득하고, 현재 충남대학교 자치행정학과 교수로 재직중임. 주요 관심분야는 규제정책, 정부기업관계, 지방재정 등이며 주요저술로는 [시민행정과 정부](공저, 2001), ‘지방정치의 변화와 자발적 조직의 역할’(1999), ‘지방정부간 경제협력 증진 방안 - 대전․충남지역을 중심으로 -’(2002), ‘재벌규제정책 실패사례로서의 주력업체제도’(2005), ‘시민참여형 도심재생모델의 정립’(2007) 등이 있음.

<E-mail: shinhg@cnu.ac.kr/논문접수일: 2008. 1. 10/심사개시일: 2008. 1. 18/심사완료일: 2008. 2. 18>