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Essays on Bargaining and Social Choice

Torstensson, Pär LU (2004) In Lund Economic Studies no. 123.
Abstract (Swedish)
Popular Abstract in Swedish

Avhandlingen består av tre teoretiska uppsatser inom förhandlingsteori och Social choice. Den första uppsatsen försöker bibehålla den entydiga jämvikten i Rubinsteins förhandlingsmodell när man utökar förhandlingsspelet till att omfatta fler än två spelare. Vi åstadkommer en entydig delspelsperfekt jämvikt i en förhandlingsmodell med tre spelare genom att anta att spelarna lägger sina bud medurs och att de praktiserar ”good-faith bargaining”. Good-faith bargaining innebär att man inte får höja sina bud när man väl har lagt ett bud i förhandlingarna. I jämvikt nås avtal i första perioden av förhandlingarna. När diskonteringsfaktorn går mot 1, är avtalet en jämn fördelning av ”kakan” som det... (More)
Popular Abstract in Swedish

Avhandlingen består av tre teoretiska uppsatser inom förhandlingsteori och Social choice. Den första uppsatsen försöker bibehålla den entydiga jämvikten i Rubinsteins förhandlingsmodell när man utökar förhandlingsspelet till att omfatta fler än två spelare. Vi åstadkommer en entydig delspelsperfekt jämvikt i en förhandlingsmodell med tre spelare genom att anta att spelarna lägger sina bud medurs och att de praktiserar ”good-faith bargaining”. Good-faith bargaining innebär att man inte får höja sina bud när man väl har lagt ett bud i förhandlingarna. I jämvikt nås avtal i första perioden av förhandlingarna. När diskonteringsfaktorn går mot 1, är avtalet en jämn fördelning av ”kakan” som det förhandlas om. Den andra uppsatsen fokuserar på det faktum att människor tycks använda konventioner snarare än strategiska resonemang när de koordinerar sina handlingar till avtal. Vi letar efter kandidater för en sådan konvention i ett två-personers förhandlingsspel med ett utomstående alternativ, dvs. en av spelarna kan hoppa av förhandlingarna och ta ett alternativ som ligger utanför spelet. Vi använder oss av begreppet ”modifierad evolutionärt stabil strategi” (MESS), vilket tar hänsyn både till hur bra och hur enkel en strategi är, för att hitta möjliga konventioner i spelet. Strategier beskrivs som automater och deras komplexitet mäts genom att räkna antalet tillstånd de har. Det visar sig att ganska många avtal kan stödjas med MESS automater; från det avtal som ger allt till spelaren med alternativet till det avtal som endast ger spelaren med alternativet en likvärdig kompensation för att inte hoppa av förhandlingarna. Detta förutsätter att alternativet är mer värt än halva ”kakan” som skall fördelas. För spel då detta villkor inte är uppfyllt visar vi existensen av MESS i spelet. Den tredje uppsatsen karakteriserar strategisäkra mekanismer för sociala val rörande allokeringen av en mångfaldig offentlig vara. Om den offentliga varan består av flera kategorier, preferenserna är separabla och mekanismen endast behöver vara surjektiv med avseende på de enskilda komponenterna och inte alla kombinationer av komponenter, kan inte Gibbard-Satterthwaite teoremet direkt appliceras. Vi finner att om mekanismens värdemängd kan omstruktureras (i kategorier) är mekanismen diktatorisk inom varje kategori av den omstrukturerade värdemängden. Vi visar att den maximala omstrukturering av värdemängden är entydig och att mekanismen är diktatorisk i de fall där värdemängden inte kan omstruktureras i kategorier. Om däremot en kategori av värdemängden bara har två alternativ så finns det icke-diktatoriska mekanismer, t.ex. röstning genom kommittéer. (Less)
Abstract
This thesis consists of three theoretical essays on Bargaining and Social Choice. The first essay addresses the problem of retaining the uniqueness of equilibrium when extending the Rubinstein model to accommodate more than two players. We achieve a unique subgame perfect equilibrium in a bargaining model with three players by assuming that the players make demands in a clockwise order and practice good-faith bargaining. Good-faith bargaining implies that they may not subsequently raise their demands. In equilibrium, agreement is reached in the first period. In the limit, as the discount factor approaches unity, the agreement is an equal split of the surplus (i.e. a third each). The second essay addresses the fact that people seems to use... (More)
This thesis consists of three theoretical essays on Bargaining and Social Choice. The first essay addresses the problem of retaining the uniqueness of equilibrium when extending the Rubinstein model to accommodate more than two players. We achieve a unique subgame perfect equilibrium in a bargaining model with three players by assuming that the players make demands in a clockwise order and practice good-faith bargaining. Good-faith bargaining implies that they may not subsequently raise their demands. In equilibrium, agreement is reached in the first period. In the limit, as the discount factor approaches unity, the agreement is an equal split of the surplus (i.e. a third each). The second essay addresses the fact that people seems to use conventions (or fairness-norms) rather than strategic reasoning when coordinating their actions to an agreement. We look for candidates for such a convention in an alternating-offers bargaining game with outside option. The concept of a modified evolutionary stable strategy (MESS), which takes complexity as well as payoff considerations, is used to derive evolutionary stable strategies. Strategies are modeled as automata and complexity is measured by the number of states an automaton has. It turns out that quite a few partitions can be supported by a MESS automaton, in fact all that lie between the outside option principle partition and the partition that assigns the entire “pie” to the player with the outside option, given that the outside option exceeds half the pie. For a bargaining game in which the outside option is not greater than half the pie, we establish the existence of a MESS.



The third essay characterize strategy-proof social choice functions (SCF:s) for the allocation of multiple public goods. If the public good is composed of several categories, preferences are separable and the SCF only has to be coordinate-wise onto, then the Gibbard-Satterthwaite theorem cannot directly be applied. We find that if the range of SCF is decomposable, it is uniquely decomposed and the SCF is dictatorial in each component of the range. If the range cannot be decomposed, then the SCF is dictatorial. If, however, a component of the range only has two alternatives (we assume at least three) then there are non-dictatorial SCF:s, e.g. voting by committees. (Less)
Please use this url to cite or link to this publication:
author
opponent
  • Shaked, Avner, Professor, Bonn University
organization
publishing date
type
Thesis
publication status
published
subject
keywords
economic systems, economic policy, Nationalekonomi, ekonometri, ekonomisk teori, ekonomiska system, ekonomisk politik, economic theory, econometrics, Economics, Coordinate-wise onto., Strategy-proof, Convention, Evolutionary stability, Subgame perfect equilibrium, Bargaining
in
Lund Economic Studies
volume
no. 123
pages
114 pages
publisher
Department of Economics, Lund Universtiy
defense location
EC3:210, Holger Crafoord Ekonomicentrum
defense date
2004-12-18 10:15
ISSN
0460-0029
language
English
LU publication?
yes
id
513ba2a3-4299-4029-a340-362a2f79b68c (old id 467530)
date added to LUP
2007-09-27 12:05:31
date last changed
2016-09-19 08:44:59
@phdthesis{513ba2a3-4299-4029-a340-362a2f79b68c,
  abstract     = {This thesis consists of three theoretical essays on Bargaining and Social Choice. The first essay addresses the problem of retaining the uniqueness of equilibrium when extending the Rubinstein model to accommodate more than two players. We achieve a unique subgame perfect equilibrium in a bargaining model with three players by assuming that the players make demands in a clockwise order and practice good-faith bargaining. Good-faith bargaining implies that they may not subsequently raise their demands. In equilibrium, agreement is reached in the first period. In the limit, as the discount factor approaches unity, the agreement is an equal split of the surplus (i.e. a third each). The second essay addresses the fact that people seems to use conventions (or fairness-norms) rather than strategic reasoning when coordinating their actions to an agreement. We look for candidates for such a convention in an alternating-offers bargaining game with outside option. The concept of a modified evolutionary stable strategy (MESS), which takes complexity as well as payoff considerations, is used to derive evolutionary stable strategies. Strategies are modeled as automata and complexity is measured by the number of states an automaton has. It turns out that quite a few partitions can be supported by a MESS automaton, in fact all that lie between the outside option principle partition and the partition that assigns the entire “pie” to the player with the outside option, given that the outside option exceeds half the pie. For a bargaining game in which the outside option is not greater than half the pie, we establish the existence of a MESS.<br/><br>
<br/><br>
The third essay characterize strategy-proof social choice functions (SCF:s) for the allocation of multiple public goods. If the public good is composed of several categories, preferences are separable and the SCF only has to be coordinate-wise onto, then the Gibbard-Satterthwaite theorem cannot directly be applied. We find that if the range of SCF is decomposable, it is uniquely decomposed and the SCF is dictatorial in each component of the range. If the range cannot be decomposed, then the SCF is dictatorial. If, however, a component of the range only has two alternatives (we assume at least three) then there are non-dictatorial SCF:s, e.g. voting by committees.},
  author       = {Torstensson, Pär},
  issn         = {0460-0029},
  keyword      = {economic systems,economic policy,Nationalekonomi,ekonometri,ekonomisk teori,ekonomiska system,ekonomisk politik,economic theory,econometrics,Economics,Coordinate-wise onto.,Strategy-proof,Convention,Evolutionary stability,Subgame perfect equilibrium,Bargaining},
  language     = {eng},
  pages        = {114},
  publisher    = {Department of Economics, Lund Universtiy},
  school       = {Lund University},
  series       = {Lund Economic Studies},
  title        = {Essays on Bargaining and Social Choice},
  volume       = {no. 123},
  year         = {2004},
}