Sex allocation conflict in ants: when the queen rules.

Insect societies are paramount examples of cooperation, yet they also harbor internal conflicts whose resolution depends on the power of the opponents. The male-haploid, female-diploid sex-determining system of ants causes workers to be more related to sisters than to brothers, whereas queens are equally related to daughters and sons. Workers should thus allocate more resources to females than to males, while queens should favor an equal investment in each sex. Female-biased sex allocation and manipulation of the sex ratio during brood development suggest that workers prevail in many ant species. Here, we show that queens of Formica selysi strongly influenced colony sex allocation by biasing the sex ratio of their eggs. Most colonies specialized in the production of a single sex. Queens in female-specialist colonies laid a high proportion of diploid eggs, whereas queens in male-specialist colonies laid almost exclusively haploid eggs, which constrains worker manipulation. However, the change in sex ratio between the egg and pupae stages suggests that workers eliminated some male brood, and the population sex-investment ratio was between the queens' and workers' equilibria. Altogether, these data provide evidence for an ongoing conflict between queens and workers, with a prominent influence of queens as a result of their control of egg sex ratio.

Dispersal and Inbreeding Avoidance.

Using a game-theoretical approach, we investigate the dispersal patterns expected if inbreeding avoidance were the only reason for dispersal. The evolutionary outcome is always complete philopatry by one sex. The rate of dispersal by the other sex depends on patch size and mating system, as well as inbreeding and dispersal costs. If such costs are sex independent, then two stable equilibria coexist (male or female philopatry), with symmetric domains of attraction. Which sex disperses is determined entirely by history, genetic drift, and gene flow. An asymmetry in costs makes one domain of attraction extend at the expense of the other. In such a case, the dispersing sex might also be, paradoxically, the one that incurs the higher dispersal costs. As asymmetry increases, one equilibrium eventually disappears, which may result in a sudden evolutionary shift in the identity of the dispersing sex. Our results underline the necessity to control for phylogenetic relationships (e.g., through the use of independent-comparisons methods) when investigating empirical trends in dispersal. Our model also makes quantitative predictions on the rate of dispersal by the dispersing sex and suggests that inbreeding avoidance may only rarely be the sole reason for dispersal.

Trace element distribution among rock-forming minerals from metamorphosed to partially molten basic igneous rocks in a contact aureole (Fuerteventura, Canaries)

Low pressure partial melting of basanitic and ankaramitic dykes gave rise to unusual, zebra-like migmatites, in the contact aureole of a layered pyroxenite-gabbro intrusion, in the root zone of an ocean island (Basal Complex, Fuerteventura, Canary Islands). These migmatites are characterised by a dense network of closely spaced, millimetre-wide leucocratic segregations. Their mineralogy consists of plagioclase (An(32-36)), diopside, biotite, oxides (magnetite, ilmenite), +/-amphibole, dominated by plagioclase in the leucosome and diopside in the melanosome. The melanosome is almost completely recrystallised, with the preservation of large, relict igneous diopside phenocrysts in dyke centres. Comparison of whole-rock and mineral major- and trace-element data allowed us to assess the redistribution of elements between different mineral phases and generations during contact metamorphism and partial melting. Dykes within and outside the thermal aureole behaved like closed chemical systems. Nevertheless, Zr, Hf, Y and REEs were internally redistributed, as deduced by comparing the trace element contents of the various diopside generations. Neocrystallised diopside - in the melanosome, leucosome and as epitaxial phenocryst rims - from the migmatite zone, are all enriched in Zr, Hf, Y and REEs compared to relict phenocrysts. This has been assigned to the liberation of trace elements on the breakdown of enriched primary minerals, kaersutite and sphene, on entering the thermal aureole. Major and trace element compositions of minerals in migmatite melanosomes and leucosomes are almost identical, pointing to a syn- or post-solidus reequilibration on the cooling of the migmatite terrain i.e. mineral-melt equilibria were reset to mineral-mineral equilibria. (C) 2007 Elsevier B.V. All rights reserved.

A case for hornblende dominated fractionation of arc magmas: the Chelan Complex (Washington Cascades)

Amphibole fractionation in the deep roots of subduction-related magmatic arcs is a fundamental process for the generation of the continental crust. Field relations and geochemical data of exposed lower crustal igneous rocks can be used to better constrain these processes. The Chelan Complex in the western U. S. forms the lowest level of a 40-km thick exposed crustal section of the North Cascades and is composed of olivine websterite, pyroxenite, hornblendite, and dominantly by hornblende gabbro and tonalite. Magmatic breccias, comb layers and intrusive contacts suggest that the Chelan Complex was build by igneous processes. Phase equilibria, textural observations and mineral chemistry yield emplacement pressures of similar to 1.0 GPa followed by isobaric cooling to 700 degrees C. The widespread occurrence of idiomorphic hornblende and interstitial plagioclase together with the lack of Eu anomalies in bulk rock compositions indicate that the differentiation is largely dominated by amphibole. Major and trace element modeling constrained by field observations and bulk chemistry demonstrate that peraluminous tonalite could be derived by removing successively 3% of olivine websterite, 12% of pyroxene hornblendite, 33% of pyroxene hornblendite, 19% of gabbros, 15% of diorite and 2% tonalite. Peraluminous tonalite with high Sr/Y that are worldwide associated with active margin settings can be derived from a parental basaltic melt by crystal fractionation at high pressure provided that amphibole dominates the fractionation process. Crustal assimilation during fractionation is thus not required to generate peraluminous tonalite.

Three essays in incomplete contracts

General Introduction These three chapters, while fairly independent from each other, study economic situations in incomplete contract settings. They are the product of both the academic freedom my advisors granted me, and in this sense reflect my personal interests, and of their interested feedback. The content of each chapter can be summarized as follows: Chapter 1: Inefficient durable-goods monopolies In this chapter we study the efficiency of an infinite-horizon durable-goods monopoly model with a fmite number of buyers. We find that, while all pure-strategy Markov Perfect Equilibria (MPE) are efficient, there also exist previously unstudied inefficient MPE where high valuation buyers randomize their purchase decision while trying to benefit from low prices which are offered once a critical mass has purchased. Real time delay, an unusual monopoly distortion, is the result of this attrition behavior. We conclude that neither technological constraints nor concern for reputation are necessary to explain inefficiency in monopolized durable-goods markets. Chapter 2: Downstream mergers and producer's capacity choice: why bake a larger pie when getting a smaller slice? In this chapter we study the effect of downstream horizontal mergers on the upstream producer's capacity choice. Contrary to conventional wisdom, we find anon-monotonic relationship: horizontal mergers induce a higher upstream capacity if the cost of capacity is low, and a lower upstream capacity if this cost is high. We explain this result by decomposing the total effect into two competing effects: a change in hold-up and a change in bargaining erosion. Chapter 3: Contract bargaining with multiple agents In this chapter we study a bargaining game between a principal and N agents when the utility of each agent depends on all agents' trades with the principal. We show, using the Potential, that equilibria payoffs coincide with the Shapley value of the underlying coalitional game with an appropriately defined characteristic function, which under common assumptions coincides with the principal's equilibrium profit in the offer game. Since the problem accounts for differences in information and agents' conjectures, the outcome can be either efficient (e.g. public contracting) or inefficient (e.g. passive beliefs).

Compact thermal storage: a-state-of-the-art review of experimental results

Thermal energy storage (TES) can increase the thermal energy effieresa, of a process by reusing the waste heat from industrial process, solar energy or other sources. There are different ways to store thermal energy: by sensible heat, by latest heat, by sorption process or by chemical reaction. This thesrs provides a-state-of-the-art review of the experimental performance of TES systems based on solid gas sorption process and chemical reactions. The importance of theses processes is that provides a heat loss free storage system with a high energy density.

Influence of stationary phase and eluent properties on chromatographic separation of carbohydrates

In this thesis, the sorption and elastic properties of the cation-exchange resins were studied to explain the liquid chromatographic separation of carbohydrates. Na+, Ca2+ and La3+ form strong poly(styrene-co-divinylbenzene) (SCE) as well as Na+ and Ca2+ form weak acrylic (WCE) cation-exchange resins at different cross-link densities were treated within this work. The focus was on the effects of water-alcohol mixtures, mostly aqueous ethanol, and that of the carbohydrates. The carbohydrates examined were rhamnose, xylose, glucose, fructose, arabinose, sucrose, xylitol and sorbitol. In addition to linear chromatographic conditions, non-linear conditions more typical for industrial applications were studied. Both experimental and modeling aspectswere covered. The aqueous alcohol sorption on the cation-exchangers were experimentally determined and theoretically calculated. The sorption model includes elastic parameters, which were obtained from sorption data combined with elasticity measurements. As hydrophilic materials cation-exchangers are water selective and shrink when an organic solvent is added. At a certain deswelling degree the elastic resins go through glass transition and become as glass-like material. Theincreasing cross-link level and the valence of the counterion decrease the sorption of solvent components in the water-rich solutions. The cross-linkage or thecounterions have less effect on the water selectivity than the resin type or the used alcohol. The amount of water sorbed is higher in the WCE resin and, moreover, the WCE resin is more water selective than the corresponding SCE resin. Theincreased aliphatic part of lower alcohols tend to increase the water selectivity, i.e. the resins are more water selective in 2-propanol than in ethanol solutions. Both the sorption behavior of carbohydrates and the sorption differences between carbohydrates are considerably affected by the eluent composition and theresin characteristics. The carbohydrate sorption was experimentally examined and modeled. In all cases, sorption and moreover the separation of carbohydrates are dominated by three phenomena: partition, ligand exchange and size exclusion. The sorption of hydrophilic carbohydrates increases when alcohol is added into the eluent or when carbohydrate is able to form coordination complexes with the counterions, especially with multivalent counterions. Decreasing polarity of the eluent enhances the complex stability. Size exclusion effect is more prominent when the resin becomes tighter or carbohydrate size increases. On the other hand,the elution volumes between different sized carbohydrates decreases with the decreasing polarity of the eluent. The chromatographic separation of carbohydrateswas modeled, using rhamnose and xylose as target molecules. The thermodynamic sorption model was successfully implemented in the rate-based column model. The experimental chromatographic data were fitted by using only one adjustable parameter. In addition to the fitted data also simulated data were generated and utilized in explaining the effect of the eluent composition and of the resin characteristics on the carbohydrate separation.

Modeling of non-isothermalvapor membrane separation with thermodynamic models and generalized mass transfer equations

A rigorous unit operation model is developed for vapor membrane separation. The new model is able to describe temperature, pressure, and concentration dependent permeation as wellreal fluid effects in vapor and gas separation with hydrocarbon selective rubbery polymeric membranes. The permeation through the membrane is described by a separate treatment of sorption and diffusion within the membrane. The chemical engineering thermodynamics is used to describe the equilibrium sorption of vapors and gases in rubbery membranes with equation of state models for polymeric systems. Also a new modification of the UNIFAC model is proposed for this purpose. Various thermodynamic models are extensively compared in order to verify the models' ability to predict and correlate experimental vapor-liquid equilibrium data. The penetrant transport through the selective layer of the membrane is described with the generalized Maxwell-Stefan equations, which are able to account for thebulk flux contribution as well as the diffusive coupling effect. A method is described to compute and correlate binary penetrant¿membrane diffusion coefficients from the experimental permeability coefficients at different temperatures and pressures. A fluid flow model for spiral-wound modules is derived from the conservation equation of mass, momentum, and energy. The conservation equations are presented in a discretized form by using the control volume approach. A combination of the permeation model and the fluid flow model yields the desired rigorous model for vapor membrane separation. The model is implemented into an inhouse process simulator and so vapor membrane separation may be evaluated as an integralpart of a process flowsheet.

Ion-exchange resins as stationary phase in reactive chromatography

Dynamic behavior of bothisothermal and non-isothermal single-column chromatographic reactors with an ion-exchange resin as the stationary phase was investigated. The reactor performance was interpreted by using results obtained when studying the effect of the resin properties on the equilibrium and kinetic phenomena occurring simultaneously in the reactor. Mathematical models were derived for each phenomenon and combined to simulate the chromatographic reactor. The phenomena studied includes phase equilibria in multicomponent liquid mixture¿ion-exchange resin systems, chemicalequilibrium in the presence of a resin catalyst, diffusion of liquids in gel-type and macroporous resins, and chemical reaction kinetics. Above all, attention was paid to the swelling behavior of the resins and how it affects the kinetic phenomena. Several poly(styrene-co-divinylbenzene) resins with different cross-link densities and internal porosities were used. Esterification of acetic acid with ethanol to produce ethyl acetate and water was used as a model reaction system. Choosing an ion-exchange resin with a low cross-link density is beneficial inthe case of the present reaction system: the amount of ethyl acetate as well the ethyl acetate to water mole ratio in the effluent stream increase with decreasing cross-link density. The enhanced performance of the reactor is mainly attributed to increasing reaction rate, which in turn originates from the phase equilibrium behavior of the system. Also mass transfer considerations favor the use ofresins with low cross-link density. The diffusion coefficients of liquids in the gel-type ion-exchange resins were found to fall rapidly when the extent of swelling became low. Glass transition of the polymer was not found to significantlyretard the diffusion in sulfonated PS¿DVB ion-exchange resins. It was also shown that non-isothermal operation of a chromatographic reactor could be used to significantly enhance the reactor performance. In the case of the exothermic modelreaction system and a near-adiabatic column, a positive thermal wave (higher temperature than in the initial state) was found to travel together with the reactive front. This further increased the conversion of the reactants. Diffusion-induced volume changes of the ion-exchange resins were studied in a flow-through cell. It was shown that describing the swelling and shrinking kinetics of the particles calls for a mass transfer model that explicitly includes the limited expansibility of the polymer network. A good description of the process was obtained by combining the generalized Maxwell-Stefan approach and an activity model that was derived from the thermodynamics of polymer solutions and gels. The swelling pressure in the resin phase was evaluated by using a non-Gaussian expression forthe polymer chain length distribution. Dimensional changes of the resin particles necessitate the use of non-standard mathematical tools for dynamic simulations. A transformed coordinate system, where the mass of the polymer was used as a spatial variable, was applied when simulating the chromatographic reactor columns as well as the swelling and shrinking kinetics of the resin particles. Shrinking of the particles in a column leads to formation of dead volume on top of the resin bed. In ordinary Eulerian coordinates, this results in a moving discontinuity that in turn causes numerical difficulties in the solution of the PDE system. The motion of the discontinuity was eliminated by spanning two calculation grids in the column that overlapped at the top of the resin bed. The reactive and non-reactive phase equilibrium data were correlated with a model derived from thethermodynamics of polymer solution and gels. The thermodynamic approach used inthis work is best suited at high degrees of swelling because the polymer matrixmay be in the glassy state when the extent of swelling is low.

Synteesikaasun liukoisuus ja aineensiirto fermentointiliuokseen

Työssä tutkittiin synteesikaasun komponenttien: hiilimonoksidin, vedyn ja hiilidioksidin liukoisuutta ja aineensiirtonopeutta fermentointiliuokseen. Kirjallisuusosassa käsitellään kaasujen liukoisuuksiin ja kaasu-nesteaineensiirtoon vaikuttavia tekijöitä ja esitellään korrelaatioita, jotka on kehitetty volumetrisen aineensiirtokertoimen ennustamiseen sekoitetussa fermentorissa. Kirjallisuus-osassa esitetään myös synteesikaasun komponenttien liukoisuudet veteen, etanoliin ja etikkahappoon 37 ºC lämpötilassa ja esitellään Flowbat-simulointiohjelman MHV2-mallin käyttöä kaasu-neste tasapainojen mallin-nuksessa. Työn kokeellisessa osassa tutkittiin synteesikaasun komponenttien liukoisuuksia veteen ja kasvatusalustaan sekä kehitettiin mittausmenetelmä kaasu-neste tasapainojen mittaukseen. Tasapainomittauksissa tutkittiin etanolin ja etikkahapon konsentraatioiden vaikutusta synteesikaasun liukoisuuteen. Lisäksi mallinnettiin kaasu-neste tasapainoja monikomponenttisysteemeissä MHV2-mallin avulla. Kokeellisen osan aineensiirtomittauksissa tutkittiin sekoitusnopeuden ja kaasun volumetrisen syöttönopeuden vaikutusta hiilimonoksidin ja vedyn volumetriseen aineensiirtokertoimeen kLa kahden litran tilavuuksisessa laboratoriofermentorissa. Mittaustulosten perusteella kasvatusalustan komponentit vaikuttavat merkittävästi hiilidioksidin liukoisuuteen. Lisäys etanolin ja etikkahapon konsentraatioissa parantaa hiilimonoksidin liukoisuutta kasvatusalustaan. Kaasun volumetrinen syöttönopeus ja sekoitusnopeus vaikuttavat voimakkaasti volumetrisen aineensiirtokertoimen arvoon. Tutkitussa systeemissä korkein teoreettinen solutiheys, joka voitiin saavuttaa suurimmalla hiilimonoksidin aineensiirto-nopeudella, oli 3 g/L. Tämä on kaksinkertainen verrattuna aiemmissa VTT:n kokeissa saavutettuihin solutiheyksiin.

Koboltin ja nikkelin poisto sinkkisulfaattiliuoksesta ioninvaihdolla

Työssä tutkittiin kahden silikapohjaisen erotusmateriaalin soveltuvuutta nikkelin ja koboltin poistoon sinkkisulfaattiliuoksista. Suurin osa kokeista tehtiin ioninvaihtimella, jonka funktionaalinen ryhmä on iminodietikkahappo. Vertailuerotusmateriaalin toiminta perustui adsorptioon. Liuoksina käytettiin sekä autenttista prosessiliuosta että synteettistä ZnSO4-liousta. Ioninvaihtimen kestävyyskokeissa selvisi, että tutkittu ioninvaihdin kestää hyvin sekä 60 oC lämpötilan että happamia olosuhteita. Emäksisissä liuoksissa silikarunko ei kestä. Jo 0,1 M NaOH-liuos liuottaa merkittävästi hartsia vuorokauden aikana. Vaihtimen vetyionikapasiteetiksi saatiin titrauksella 2,3 mekv/g. Tasapainokokeilla saatiin selville, että ioninvaihdin on selektiivinen nikkelille sinkin suhteen ja että selektiivisyys kasvaa liuoksen pH:n laskiessa. Koboltille ioninvaihdin ei ole selektiivinen sinkin suhteen. Mikäli sinkin pitoisuus on tuhansia kertoja nikkelin pitoisuutta suurempi, ei ioninvaihtimen Ni-selektiivisyys riitä myöskään nikkelille. Synteettisillä ZnSO4-liuoksilla tehtyjen kolonnikokeiden perusteella havaittiin, että tutkitulla ioninvaihtimella voidaan laimeista ZnSO4-liuoksista poistaa nikkeliä selektiivisesti. Nikkelin eluointi onnistui helposti 1 M H2SO4:lla. Vertailukokeen perusteella oli ioninvaihtimen Ni/Zn-selektiivisyys referenssiadsorbentin Ni/Zn-selektiivisyyttä pienempi. Ioninvaihtokolonnin mallintaminen ei onnistunut riittävän hyvin kuvaamaan ioninvaihtimessa tapahtuvaa samanaikaista ioninvaihtoa ja adsorptiota. Sen sijaan kun kolonnissa oli vertailumateriaalina käytetty adsorbentti, saatiin kolonnikokeiden tulokset mallilla hyvin ennustettua.

Erikoispaperin käyristymisen pienentäminen mittapysyvyyttä parantamalla

Diplomityössä on tutkittu Tervakoski Oy:n PK8:lla valmistettavan irrokepaperin mittapy-syvyysongelmaa. Tämä ilmenee asiakkaan jatkojalostusprosesseissa esim. silikonointi- ja liimausvaiheissa paperin huonona ajettavuutena. Työ pohjautuu PK8:lla suoritettavien tehdasmittakaavaisten koeajojen prosessiolosuhteiden ja mittapysyvyyttä kuvaavien analyysien tulosten tarkasteluun. Työn kirjallisuusosassa kerrotaan silikonointi- ja laminointiprosessin vaatimuksista irrokepaperille. Mittapysyvyyden teoreettista taustaa lähestytään puukuidun sorptio-ominaisuuksien tarkastelulla. Osassa perehdytään mm. paperin mittapysyvyyteen ja käyristymiseen vaikuttaviin eri tekijöihin. Osio sisältää myös katsauksen paperin mittapysyvyyden ja käyristymisen eri mittausmenetelmistä. Työn kokeellisessa osassa tarkastellaan PK8:n prosessiolosuhteiden vaikutuksia mittapysy- vyyden tasoon. Kokeellinen osa sisältää neljä tehdasmittakaavaista koeajosarjaa ja 23 eri koepistettä, joiden tarkoituksena on löytää PK8:lle mittapysyvyyden kannalta parhaimmat mahdolliset olosuhteet muiden laatuarvojen kärsimättä. Koesarjojen muuttujina on käytetty kuivatusviirojen kireyttä, konesuuntaista vetojännitystä sekä suihkusuhteen ja jauhatusasteen muutoksia. Lisäksi paperin käyristymiseen pyrittiin vaikuttamaan PK8:lla toispuoleisella kuivatuksella ja erilliskostutuskoneen toispuoleisella kostutusvesimäärällä. Koesarjojen prosessiolosuhteiden ja analyysitulosten perusteella PK8:lla muutettiin ajotapamallia jo työn kuluessa. Kokeellisen osan loputtua PK8:n tuotantolinjalle määriteltiin uusi ajotapamalli. PK8:n tuotantolinjalla valmistettavan glassiinin poikkisuuntainen kuivatuskutistuma aleni eräässä koesarjassa prosessiolosuhteiden muutosten myötä noin 13 %. Mittapysy-vyyttä kuvaavat kosteuslaajentuma, märkämuodonmuutos ja käyristyminen paranivat keskimäärin 11 %. Uuden ajotapamallin myötä PK8:n valmistaman irrokepaperin laatutaso on noussut, jolloin on jo nyt havaittu, että glassiinin ajettavuus on selkeästi parantunut asiakkaan jatkojalostusprosesseissa.

Nesteseosten liukoisuuksien mittaaminen

Diplomityön tarkoituksena on tarkastella isobuteenin dimeroitumisprosessin neste-nestetasapainoja. Tavoitteena on määrittää prosessissa esiintyvien komponenttien väliset neste-nestetasapainot. Työn kirjallisuusosassa on tarkasteltu neste-nestetasapainojen teoriaa. Erityisesti on tarkasteltu mittausmenetelmiä sekä kirjallisuudesta löytyneitä laitteistoja binääristen ja ternääristen systeemien neste-nestetasapainojen määritystä varten. Menetelmät ja laitteistot on esitetty erikseen matalassa ja korkeassa paineessa suoritettaville mittauksille. Lisäksi on tarkasteltu näytteenottoa sekä näytteiden analysointimenetelmiä. Kirjallisuusosassa on myös sivuttu kaasu-neste-nestetasapainojen määritystä, mutta työn varsinainen kohde on neste-nestetasapainojen määritys. Työn kokeellisessa osassa määritettiin iso-oktaaniprosessissa esiintyvien komponenttien välisiä binäärisiä ja ternäärisiä neste-nestetasapainoja. Mitattavien komponenttiparien määrää karsittiin ja jäljellejääneiden parien välillä suoritettavat mittaukset jaoteltiin matalassa ja korkeassa paineessa suoritettaviin määrityksiin. Ternääriset mittaukset tulivat kyseeseen sellaisten komponenttiparien kohdalla, joissa toisiinsa täysin liukenevien nesteiden systeemiin kolmatta komponenttia lisättäessä saatiin aikaiseksi kaksi nestefaasia. Tällaisesta mittaustiedosta voidaan määrittää neste-nestetasapainomallien parametrejä. Mittausten lisäksi kokeellisessa osassa tarkasteltiin näytteenottoa sekä näytteiden analysointia.

Safety Traps

Fear of risk provides a rationale for protracted economic downturns. We develop a real business cycle model where investors with decreasing relative risk aversion choose between a risky and a safe technology that exhibit decreasing returns. Because of a feedback effect from the interest rate to risk aversion, two equilibria can emerge: a standard equilibrium and a "safe" one in which investors invest in safer assets. We refer to the dynamics of this second equilibrium as a safety trap because it is self-reinforcing as investors accumulate more wealth and show it to be consistent with Japan's lost decade.

One-seller assignment markets with multi-unit demands

We consider one-seller assignment markets with multi-unit demands and prove that the associated game is buyers-submodular. Therefore the core is non-empty and it has a lattice structure which contains the allocation where every buyer receives his marginal contribution. We prove that in this kind of market, every pairwise-stable outcome is associated to a competitive equilibrium and viceversa. We study conditions under which the buyers-optimal and the seller-optimal core allocations are competitive equilibrium payoff vectors. Moreover, we characterize the markets for which the core coincidences with the set of competitive equilibria payoff vectors. When agents behave strategically, we introduce a procedure that implements the buyers-optimal core allocation as the unique subgame perfect Nash equilibrium outcome.