Two remarks are in order. First, according to Kautilya, wise kings (individuals) didn’t put all their soldiers at one place and also did not indulge in gambling and other vices. Secondly, he showed awareness of a backward bending supply curve (‘enjoying his success is to become negligent’).
Mobilization of No More Than Three-Fourths of the Army: He further emphasized diversification. He (p 629) stated, ‘A conqueror, having assured himself about his superiority in power, place and time, shall first leave behind a third or a quarter of his army to protect his capital, the rear, the forest regions and the borders; he shall then march towards the enemy taking with him enough wealth and forces to help him achieve his objective (9.1).’ He wanted territorial expansion, subject to the preservation of existing territory. He advanced the basic principle: not to invest hundred percent in a risky venture. Although the context has changed, but the goal of risk reduction through diversification is an invariant one.7
19.4 MULTI-VARIABLE APPROACH TO SUCCESS OF A CAMPAIGN Power, Place and Time: Kautilya (Kangle (Part II, p 407-408)) reviewed the relative importance of various factors as: ‘“Of power, place and time, however, power is superior”, say the teachers. For, one possessed of power is able to counter-act (the difficulties of ) marshy or dry region and (those) of time with cold, heat or rain. “Place is superior”, say some. For, a dog on land drags a crocodile; a crocodile in water drags a dog. “Time is superior” say some (others). “By day a crow kills an owl, at night an owl kills a crow”. “No” says Kautilya. Power, place and time are mutually helpful (9.1).’
Kautilya (p 681) suggested that a king should avoid harsh conditions, such as, ‘having to fight in an unsuitable terrain and having to fight in an unsuitable season’, which might adversely affect the efficiency of the army. He believed if the goal was to maximize the probability of success of a campaign with a minimum effort, a king should consider their most favourable combination since these variables were complementary to each other. That is, a king could not afford to ignore any one of them and therefore, should not concentrate on judging their relative influences. His ideas may be expressed as:
S = α0 + α1RP1 + α2D1 + α3D2 + α4D1D2 + u
(19.1) Where D1=1 for an appropriate place
=0 otherwise Where D2=1 for an appropriate time
=0 otherwise
Where, S = success, relative power, RP1 = P1/P2 =power of king one/ power of king two (see Chapter 18 for notations) and u=random error.
According to Kautilya, the coefficient α4 in Equation 19.1 should be positive since it measures the complementary nature of time and place. Of course, he was not concerned with its specification or estimation, which might be quite challenging. Since according to him, probability of success increased more than proportionately to the increases in relative power.
SUMMARY
Kautilya’s predecessors compared only the expected returns of various
projects or assets but he explicitly incorporated the risk-return tradeoffs into his analyses related to various risky situations. He did not know how to measure variances and co-variances, yet he was aware of the possibility of risk reduction through diversification. It would seem that the ancient thinkers were as concerned about dealing with risk as we are. It is apparent that growth in economic knowledge is as much due to the advancement in probability theory and calculus as it is due to economists’ own ingenuity.8
20
Time Inconsistency Problem and Asymmetric Information
No enemy shall know his secrets. He shall, however, know all his enemy’s weaknesses. Like a tortoise, he shall draw in any limb of his that is exposed.
—Kautilya (p 177)
Although Kautilya did not provide any formal analysis on it, his informal approach contained many insights of a modern game theory. He incorporated foresight and the problem of ‘credibility’ into his analysis of strategic interactions. In fact, the application of the ‘time inconsistency’ problem in the case of a monetary policy appears to be ‘much ado about nothing’ compared to the one considered by Kautilya in which the sovereignty of a state was at stake. He emphasized the benefits of possessing asymmetric information in bargaining.
Kautilya envisaged for a king to incorporate the possibility of reoptimization by an ally into his current decision-making. Section 20.1 discusses his ideas on what nowadays is called the time inconsistency problem. He was aware of the role of asymmetric information and a few examples are presented in Section 20.2. It is shown that Kautilya applied an informal game-theoretic analysis.1 Section 20.3 elaborates on his emphasis on seeking the advantages of private information in bargaining. Kautilya’s analysis is implicit and elementary modern methods are used to make his ideas explicit.
He invariably insisted on applying the cost-benefit analysis before undertaking any project including waging a war. For example, Drekmeier (1962, p 157) observes, ‘By the age of empire (and implicit in the Arthashastra of Kautilya), war had ceased to be regarded as an aristocratic pastime having as its main objective military glory, and had come to be conceived as an instrument for strengthening the state and enriching its treasury. War is now a serious business, not to be undertaken lightly and without weighing carefully the probabilities of success and defeat.’
20.1 KAUTILYA ON TIME INCONSISTENCY PROBLEM At the time of Kautilya there was no central bank to undertake any monetary policy. Still the problem of credibility was perhaps quite serious, since not only the well being of the citizens but their independence also was at stake. It was not the public worrying about the credibility of the king but the king himself worrying about the credibility of other kings. The king needed cooperation of other kings to achieve certain objectives but faced a possible threat of a conflict in the future from the very same kings. Kautilya was acutely aware of the problem now called the problem of time inconsistency or credibility.2
Specification of a King’s Objectives: According to Kautilya, a king should undertake the cost-benefit analysis of various policies, such as, whether to carry out a campaign alone or to form an alliance and how to choose an ally. A king’s projected intermediate objective was to acquire power and ultimately enjoy prosperity and maintain independence. Kautilya (p 616) stated, ‘Before undertaking a combined operation [with the forces of other rulers] a king shall carefully consider the reasons for waging war or making peace and join forces with powerful and upright rulers.’ Further, ‘The objective of a joint campaign is to acquire an ally, wealth or land; gaining one later in the list is preferable to one earlier. A king shall enter into a treaty and undertake a joint campaign, always keeping in mind his own objective, and after analyzing the clear and definite benefit or part benefit that will accrue to him (7.5).’ Obviously, at that time, there was no opportunity for undertaking joint research ventures.
Implicit Two Period Analysis: Kautilya essentially considered a two period analysis. The policies to be adopted during the current period and the following period were analyzed right in the beginning itself. He discussed how a king should choose an ally, who helped the king achieve his current objective and did not turn against him in the future, causing loss of wealth and even his kingdom.
Insights into the Credibility Problem: The treaty must specify the contributions of King I and King II (his ally) to undertake a joint campaign and their shares in the acquisitions if there was a success in the campaign. Kautilya (p 572) stated, ‘When the shares are specified before the start of the campaign it is normal to base them on the proportion of troops contributed; however, fixing the shares on the basis of the efforts made by each one during the campaign is the best type. Shares can also be based on the money contributed by each one or the plunder seized (7.4).’ All the terms and conditions were specified before the start of the campaign. It may be noted that this specification falls under the open-loop control approach, whereas the classical approach (Bellman’s approach) is categorized as the ‘feedback or the closed-loop’ control approach.3
In the current debate on th
e credibility problem, the central bank announces its monetary policies, which maximize its objective function, subject to public’s reaction function to them. Once the public has incorporated the central bank’s policies in its decisions, the central bank might change its initially announced policies to re-optimize its objective function. That is, the central bank may not keep its initial commitment. Kautilya analyzed the possibility of reneging that the commitments made by a strong king to a weak king might not be kept. The stronger king (King II) maximized his objective function, subject to the reactions of the weaker king (King I) to his commitments. King II was assumed to maximize his objective function, G2 (r1, r2, A1, A2), which is assumed additive in the two periods. Kautilya’s informal analysis can formally be presented as follows:
Max G2 (r1, r2, A1, A2) = G2 (r1, A1) + G2 (r2, A2) (20.1)1 2
Subject to the reaction functions r1 and r2 of King I
r1 = R1 (A1, A2) (20.2)
r2 = R2 (r1, A2) (20.3)
Where G2 (r1, A1) = Objective function of King II for period 1
one, which depended on the reaction function of King I for period one and his own policies, A1 to be adopted for the first period, such as specifying his contributions towards the campaign.
G2 (r2, A2) = Objective function of King II for period two,2
which depended on the reaction function of King I for period two and his own promises, A2 to be kept for the second period, such as a promise of non-aggression and specification of shares in the seizures for period two.
Equation (20.2) indicates the reaction function, r1 of King I for period one, which depends on the policy decisions of the King II in both the periods (ie. on A1 and A2).
Equation (20.3) indicates that the reaction function, r2 of King I in period two depends on his decisions taken in period one (ie. r1) and A2.
Let A* and A* be the optimum values such that King II’s objective1 2
function was maximized subject to the reaction functions of King I.4 King II announces these policies (promises) at the beginning of period one. King I undertakes his measures, believing that king two would keep these promises. At the end of the first period (beginning of the second period), the reaction function of King I takes the form:
r* = R1 (A* , A* ).1 1 2
Possible Re-optimization by King II: Kautilya (p 624) stated, ‘The king may face dangers even from a trusted king of equal power, when the latter has achieved his objective. Even an equally powerful king tends to become stronger after the task is accomplished and, when his power has increased, becomes untrustworthy. Prosperity changes peoples’ minds (7.5).’
Kautilya was quite concerned that the commitments made by King II (the ally) before the start of the campaign may not be honoured after its completion, since the actions of King II could not be constrained by current commitments in any credible way. According to Kautilya, the relative power of a king was one of the important determinants of success in a war and consequently the non-aggression treaty agreed upon by the second king might be annulled and he might turn against King I. Also, whatever shares were specified before the start of the campaign might not be optimal after a successful campaign. According to Kautilya, King II after a successful campaign, particularly if he was equal or stronger (and not upright), might decide to re-optimize. That is, King II could re-optimize his objective function for period two as follows:
Max G2 = G2 (r2, A2) (20.4)2 2
Subject to
r2 = R2 (r* , A2) (20.5)1
Let AC be the revised policy adopted to maximize G2 in equation2 2 (20.4) subject to r2 in equation (20.5). According to Kautilya, it
was likely to be different from the initial policy A
* that is, AC ≠A*
2 2 2 and particularly, if the second king was not upright. In other words, according to Kautilya, King II was likely to cheat on his promises, implying he could attack King I or not give his due share out of the loot and land acquired through a successful campaign.
Precautionary Measures in Anticipation of Possible Reneging by King II: Kautilya suggested that King I should take defensive measures to protect his interests against the likely reneging by King II (his ally) on the contractual arrangements. He suggested specific actions to be undertaken by King I, depending on the anticipated circumstances. He (p 596) stated, ‘If a king believes that the one to whom troops are lent will, after achieving the objective for which they were hired, appropriate them himself, send them to hostile lands or jungles, or, in some fashion make them useless, the forces shall not be lent, using the pretext that they are needed elsewhere.
‘If, however, he is obliged to lend his troops, they shall be lent only for the limited period of that campaign, on condition that they shall stay and fight together and be protected from all dangers till the end of the campaign; as soon as the campaign is over, they shall be withdrawn on some pretext (7.8).’ Further (p 624), ‘If the stronger ruler is not upright, the king shall quickly withdraw under some pretext, when the work has been done. If the stronger ruler is upright, the king shall wait until he is given permission to leave. The king shall make all efforts to move away from a dangerous situation, after ensuring the safety of the queen. Even if the king receives a small share, or even no share, from a stronger king, he shall go away with a ‘seemingly’ content look. Later, when the strong king comes under the king’s power [for any reason], twice the loss shall be exacted.’
Kautilya (p 609) stated, ‘An ally who is likely to grow in power after defeating the enemy and thus become uncontrollable shall be embroiled in a conflict with his own neighbour and his own ally; or, a pretender in his family or an unjustly treated prince shall be encouraged to seize the throne; or such actions shall be taken as would oblige the ally to remain obedient, in return for help received (7.18).’
If King I was the Campaign Leader: Kautilya (p 624) suggested, ‘The king, when he himself has led the allies to victory, shall let the others go, after giving them their due shares. He should, if necessary, forgo his own share and not deprive them of theirs. It is thus that a king will win the affection of his Circle of States (7.5).’
Several points are noteworthy. First, Kautilya displayed an insight into the time inconsistency problem. His suggestion to King I comprised, taking defensive measures to protect against a possible reneging and a threat of aggression against him by King II. Kautilya was aware of the irresistible temptation, on the part of the leader of a joint campaign, to cheat his followers and advance his own objectives. Blackburn and Christensen (1989) also point out the possibility of such an outcome. They state, ‘A non-cooperative Stackelberg game possesses a definite hierarchical structure in the sense that some players (leaders) have the potential to impose their policies on others (followers).’ They add, ‘This is because of an incentive for a leader to improve his own payoff by reneging (cheating) on his promised action, an indication that the optimal policy in Stackelberg games is dynamically inconsistent.’ It also implies that every king would like to be a leader and as Nicholson (1985, p 458-459) notes, which might have disastrous consequences. Secondly, a ‘tit for tat’ motivation was also present. If the leader of a campaign (King II) did not fulfill his commitments, he should be given the same treatment whenever he came under the leadership of King I. Thirdly, Kautilya recommended to a king to build his reputation to be trustworthy, which might be an asset in maintaining or forming new coalitions in the future.
Trust as the Primary Criterion in the Selection of an Ally: Selecting a conservative Federal Reserve Bank Chairman (or Governor of a Central Bank) has been recommended to resolve the inconsistency or credibility problem. Similarly, Kautilya recommended that an ally should be upright. He ranked possible allies according to their trustworthiness, and current and future potential gains to the king. He (p 606) explained, ‘The best ally is one who has the following six qualities: an ally of the family for a long time, constant, amenable to control, powerful in his support, sharing a common interest, able to mobilize his forces quickly
and not a man who betrays his friends (7.9).’
Kautilya (p 606) elaborated on these qualities, ‘A true friend is one who shares with the king a common objective, is helpful, never changes and never double crosses even when the king is in trouble (7.9).’ Further (p 607), ‘That friend, whose friendship has endured since earlier times and who protects and is in turn protected out of love and not for mercenary reasons is called a constant ally (7.9).’
An ally should be trustworthy and capable of helping the king. However, sometimes, the choice may not be that easy. For example, some possible allies who are equal or stronger than the king may be capable of helping but not trustworthy and others may be controllable but weak.
Kautilya (p 573) held, ‘Amity with a more powerful monarch carries great danger for kings, except when one is actually at war with an enemy (7.2).’ Further (p 616), ‘As between joining forces with a ruler who is stronger than the king or with two rulers of strength equal to the king, it is better to join two equal kings. For with one ruler, the stronger ruler will have the upper hand during the campaign, whereas with two equals the king can keep control. If one of them turns treacherous, it will be easy for the other two to suppress him and make him suffer the consequences of the dissent (7.5).’
Kautilya favoured weaker kings for an alliance since they could not dare to renege on their commitments whereas equal or stronger kings might not keep their commitments. Also, if a king did not trust another king, he should try to avoid forming an alliance with him. In the light of above statements, matrix 20.1 may be used to capture his ideas regarding potential allies.5
Kautilya- the True Founder of Economics Page 33