Game Theory Term Paper

Game Theory Term Paper Anomitra Bhattacharya [email protected] edu, Cornell ID – 2316802 What ails Uttar Pradesh? The states of Uttar Pradesh (UP) and Tamil Nadu (TN) reveal a marked north-south divide in India. Uttar Pradesh, which was ahead of Tamil Nadu in the 1960s, now lags behind in the same sectors where Tamil Nadu has made significant progress. If one were to study Indian history or politics, UP’s lag would come as a surprise. All but four Prime Ministers of India have come from UP. UP has the famous Taj Mahal, the ancient & holy city of Varanasi and the confluence of Ganga and Jamuna rivers in Allahabad.

These sites are of great national and international importance. What then accounts for such a miserable record for UP? The long-term reasons are unclear, but the more recent causes are identifiable. We use game theory to explain some of these causes. For roughly two decades until 2007, no government in UP lasted throughout its term and there was no political stability. In the state elections of May 2007, the victory of the Bahujan Samaj Party (BSP), a primarily Dalit (lower caste) party under the leadership of Mayawati, finally terminated the endemic political chaos and promised political stability.

BSP won 206 of the 402 seats in the state assembly elections. Mayawati’s victory was based on an unusual social coalition. In 2007, every sixth Brahmin (higher caste) in UP voted for the BSP. Even in South India, where the non-Brahmin castes came to power in the 1960s, Dalits, the bottom of the social ladder, were never in the lead. Mayawati’s 2007 victory constituted a democratic political revolution of sorts. The BSP’s rise to power created a window of opportunity for economic development.

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In a state haunted by endemic political instability, the very promise of political stability was a positive development. Mayawati’s victory, thus, opened the possibility of a dualistic political thrust. She had the opportunity to combine the politics of dignity, the core of BSP politics thus far, and the politics of economic development, which would make it possible to serve a larger social base. But electoral realities meant that the BSP had to change their original political agenda – restoring dignity for the lower caste.

It was no longer a party that catered only to the Dalits. Rather, its emphasis on the “poor upper castes” as well as Dalits and “lower OBCs” (Other Backward Classes) meant that it needed to cater to a larger social coalition. But why did BSP cling to their tactics of the “politics of dignity”? We presume the BSP think-tank was caught in a situation where they had no incentive to deviate from their tried & tested stance of “Dignity”. We assume a sequential move game here. The players in this game were “BSP” & the “Voters”.

BSP had two strategies to adopt – the strategy of “Dignity” giving them a payoff of 10 (say) when the Voters “Accept” this strategy or a payoff of 6 (say) when they “Reject” this strategy or the strategy of “Dignity & Development” giving them a payoff of 8 (lower than 10 because of the additional effort they have to expend in promoting development). The Voters will have a payoff of 3 when they “Accept” the strategy of “Dignity” & a payoff of 2 if they “Reject” it. They get a payoff of 6 when BSP follows the strategy of “Dignity & Development”.

We construct our tree & game table below [The terminal histories for the tree is (Dignity, Accept), (Dignity, Reject) & (Dignity & Dev)] – 8, 6 | | |VOTERS |(PLAYER 2) | | | |ACCEPT |REJECT | |BSP |DIGNITY |10*, 3* |6, 2 | |(PLAYER 1) |DIGNITY & DEV |8, 6* |8*, 6* |

By using “Best Response Function” we see that there are 2 Nash Equilibrium in this game – when BSP chooses strategy “Dignity” & the Voters chooses strategy “Accept” resulting in payoffs 10 & 3 respectively for them & when BSP chooses strategy “Dignity & Development” & the Voters chooses strategy “Reject”. But in the sub-game following the history “Dignity” the optimal strategy for Voters is to choose “Accept” because of the higher payoff.

Given the Voter’s strategy, BSP would like to choose the strategy “Dignity” rather than “Dignity & Development” because it gives them a higher payoff. Thus the sub game perfect equilibrium is when BSP choose strategy “Dignity” & the Voters choose strategy “Accept”. Our analysis shows that the socially optimal outcome is when the sum of the payoffs for both the players is the highest – in this case it is 14 (8 + 6) & it occurs when BSP chooses strategy “Dignity & Development” & the Voters “Accept” it (the strategy “Reject” for the Voters is not credible).

We can only surmise that BSP’s obsession with this strategy of “Dignity” is because of their past success – they had no incentive to deviate. This is where BSP & Mayawati has badly erred. The old brand of the politics of dignity has been pursued on a grand scale. However, the politics of economic growth, which requires emphasis on governance and market-oriented policies, has been more or less neglected.

Three features have marked Mayawati’s politics of dignity – grand architectural projects aimed at making Dalit’s icons more visible in the public sphere, extension of affirmative action beyond the standard government services and public education, and the accent on behavioral retribution – using politics to punish those previously powerful (Dalit politicians often express their power by transferring officials mostly of upper caste origin at will, or by excessively punishing the violations by upper caste politicians to teach them the new grammar of respect for the lower castes).

Generating respect for lower castes as fellow citizens is a worthy endeavor, but this model of politics of dignity suffers from a crippling contradiction. Unless it is backed by a strategy to lift economic growth, it only provides symbolic benefits but does not fundamentally transform the lives of the masses. Lower caste parties in Tamil Nadu realized this much earlier and began to attend both to dignity and economic growth. Unfortunately Mayawati is still obsessed with this conventional model.

She has already paid a price for her inadequate vision. In the recently concluded union assembly elections (distinguish this from the state assembly elections), she lost votes among virtually all groups, including the upper castes that facilitated her rise to national prominence. We now analyze the results of the recently concluded union assembly elections of UP & Tamil Nadu. Although these results are for the union assembly polls, they give us some understanding of the political atmosphere in the 2 states – UNION ASSEMBLY ELECTION 2009 RESULTS | |STATES |SEATS |BREAKUP | |UTTAR PRADESH – |UP (80/80) – |INC (21), BJP (10), BSP (20), SP (23), OTHERS (6) | |  | |TAMIL NADU – |TN (39/39) – |INC (8), DMK (18), OTHERS (13) |

We calculate Shapely Value or Power Index for these parties – In the case of TN, no single party gets a majority while the groups of 2 parties getting a majority is (INC, DMK), (INC, OTHERS) & (DMK, OTHERS). In each of these groups, each party is a “pivotal member” of the majority coalition. In the case of UP, no single party gets a majority. The groups of 2 parties getting a majority are (INC, BSP), (INC, SP) & (BSP, SP). In each of these groups, each party is a “pivotal member”.

The groups of 3 parties getting a majority where the “pivotal members” are underlined in EACH parenthesis are – (INC, BSP, BJP), (INC, SP, BJP), (BSP, SP, BJP), (INC, BSP, OTHERS), (INC, SP, OTHERS), (BSP, SP, OTHERS). Similarly the groups of 4 parties getting a majority are – (INC, SP, BJP, OTHERS), (INC, BSP, BJP, OTHERS), (BSP, SP, BJP, OTHERS). Groups getting a majority but having no pivotal members are not considered. For UP (Uttar Pradesh) – Power Index INC – [(5-2)! *(2-1)! *2]/5! [(5-3)! *(3-1)! *4]/5! + [(5-4)! *(4-1)! *2]/5! = 1/3 Similarly Power Index for both BSP & SP is 1/3 while BJP & OTHERS has 0 Power Index For TN (Tamil Nadu) – Power Index DMK – [(3-2)! *(2-1)! *2]/3! = 1/3 Similarly Power Index for INC & OTHERS is calculated to be 1/3 We conclude that in UP the 3 parties INC, BSP & SP have more or less equal number of seats & equal power index of 1/3 each. Parties like BJP, in spite of 10 seats have no power index & hence fail to influence state politics.

The equal strength of 3 parties mean there is constant tussle for power with the result that political parties are more likely to devote much of their energy in garnering popular support through strategies like “Dignity” (as we have seen earlier for BSP) rather than devote their energy for “Development Work” whose gains are not realized immediately. On the other hand, in Tamil Nadu, a party like INC have seats less than half that of DMK, but have the same power index of 1/3 as that of DMK. This means INC has a considerable say in the state politics & can hold the other party accountable for its performance.

This implies that there is greater incentive for the ruling party to devote more time on better governance. Our Shapely Value analysis thus clearly reflects that Tamil Nadu is more likely to experience better governance & economic growth in the coming future rather than Uttar Pradesh. Mayawati’s failure to combine dignity with economic growth is a tragedy for UP. UP is blessed with some of the top technical and scientific institutions of India. The intellectual capital of such institutions remains untapped in the policy process.

The politicians and bureaucrats think they know it all. With agriculture and investment in roads alone, UP can’t reach a high enough growth rate. UP needs high value-added manufacturing and services industry and currently the government has no vision to get there. Moreover UP needs to effectively manage their commons. Elinor Olstrom in her work on the commons stressed the importance of polycentric governance – an approach that emphasizes the degree to which higher levels of government should not crowd out self-organization at the lower levels.

Her studies revealed that the institutional arrangements from within resulting from self-governed fish stocks, pastures, woods, lakes and groundwater basins are “more often than not, better than predicted by standard theories”. Tamil Nadu has made rapid progress in social & economic front because of effective public private partnership & a strong political commitment in managing the commons. UP lags behind in such endeavors. Unless the political parties in UP forego their internal bickering & adopt a commitment for economic development, the future looks grim.

The way Mayawati’s BSP lost in the recently concluded union elections points to something very significant. Many people did not like the way she threw her weight around, her ostentation, the dozens of statues she is erecting in her likeness, her assumption that even if she did nothing history was waiting for her. In a country highly tolerant of all forms of radicalism & diversity, Mayawati’s self aggrandizing tactics may still not stand the test of time. Indian politics has taught humility to lots of politicians before. It will teach humility & wisdom to Mayawati someday.

References Uttar Pradesh – Wikipedia, the free encyclopedia. mht Statewide Results of Lok Sabha Election 2009 – Live Update, General Elections 2009, 15th Lok Sabha Election, Indian General Elections, Live Update Election. mht http://www. asianage. com/presentation/columnisthome/govind-talwalkar/the-great-economic-north-south-divide. aspx The Challenge in Uttar Pradesh by Ashutosh Varshney Games of Strategy – Avinash Dixit & Susan Skeath An Introduction to Game Theory – Martin J Osborne ———————– VOTERS DIGNITY DIGNITY & DEV BSP 10, 3 6, 2 ACCEPT REJECT