Suppose two players wish to divide a finite set of indivisible items, over which each distributes a specified number of points. Assuming the utility of a player’s bundle is the sum of the points it assigns to the items it contains, we analyze what divisions are fair. We show that if there is an envy-free (EF) allocation of the items, two other desirable properties — Pareto-optimality (PO) and maximinality (MM) — can also be satisfied, rendering these three properties compatible, but other properties — balance (BL), maximum Nash welfare (MNW), maximum total welfare (MTW), and lexicographic optimality (LO) — may fail. If there is no EF division, as is likely, it is always possible to satisfy EFx, a weaker form of EF, but an EFx allocation may not be PO, BL, MNW, MTW, or LO. Moreover, if one player considers an item worthless (i.e., assigns zero points to it), an EFx division may be Pareto dominated by a nonEFx allocation that is MNW. Although these incompatibilities suggest that there is no “perfect” 2-person fair division of indivisible items, EFx and MNW divisions — if they give different allocations when there is no EF-PO-MM division — seem the most compelling alternatives, with EFx, we conjecture, satisfying the Rawlsian objective of helping the worse-off player and MNW, a modification of MTW, suggesting a more Benthamite view.
{"title":"Two-Person Fair Division of Indivisible Items: Compatibilities and Incompatibilities","authors":"S. Brams, M. Kilgour, Christian Klamler","doi":"10.2139/ssrn.3911298","DOIUrl":"https://doi.org/10.2139/ssrn.3911298","url":null,"abstract":"Suppose two players wish to divide a finite set of indivisible items, over which each distributes a specified number of points. Assuming the utility of a player’s bundle is the sum of the points it assigns to the items it contains, we analyze what divisions are fair. We show that if there is an envy-free (EF) allocation of the items, two other desirable properties — Pareto-optimality (PO) and maximinality (MM) — can also be satisfied, rendering these three properties compatible, but other properties — balance (BL), maximum Nash welfare (MNW), maximum total welfare (MTW), and lexicographic optimality (LO) — may fail. If there is no EF division, as is likely, it is always possible to satisfy EFx, a weaker form of EF, but an EFx allocation may not be PO, BL, MNW, MTW, or LO. Moreover, if one player considers an item worthless (i.e., assigns zero points to it), an EFx division may be Pareto dominated by a nonEFx allocation that is MNW. Although these incompatibilities suggest that there is no “perfect” 2-person fair division of indivisible items, EFx and MNW divisions — if they give different allocations when there is no EF-PO-MM division — seem the most compelling alternatives, with EFx, we conjecture, satisfying the Rawlsian objective of helping the worse-off player and MNW, a modification of MTW, suggesting a more Benthamite view.","PeriodicalId":433547,"journal":{"name":"Two-Party Negotiations eJournal","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133680787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper examines how firms’ organizational form affects prices negotiated. Negotiated prices are one factor determining whether a vendor or customer captures the value from a transaction. Firms that systematically negotiate more effectively capture more value. Research has investigated individual- and market-level determinants of negotiation outcomes, but little has been done on the firm-level determinants of negotiated prices. I present a first look at one feature, sales process: whether salespeople handle the entire sale in parallel or customers begin with less experienced salespeople who can escalate difficult assignments. I model firms’ choice of sales process as a biform game and test predictions of the model using a combination of transaction-level data on new car purchases in the U.S. and a unique survey of dealership management practices. I find that a serial process has implications consistent with improving firms’ bargaining power and reducing customers’ outside option.
{"title":"Organization and Bargaining: Sales Process Choice at Auto Dealerships","authors":"V. M. Bennett","doi":"10.1287/mnsc.1120.1691","DOIUrl":"https://doi.org/10.1287/mnsc.1120.1691","url":null,"abstract":"This paper examines how firms’ organizational form affects prices negotiated. Negotiated prices are one factor determining whether a vendor or customer captures the value from a transaction. Firms that systematically negotiate more effectively capture more value. Research has investigated individual- and market-level determinants of negotiation outcomes, but little has been done on the firm-level determinants of negotiated prices. I present a first look at one feature, sales process: whether salespeople handle the entire sale in parallel or customers begin with less experienced salespeople who can escalate difficult assignments. I model firms’ choice of sales process as a biform game and test predictions of the model using a combination of transaction-level data on new car purchases in the U.S. and a unique survey of dealership management practices. I find that a serial process has implications consistent with improving firms’ bargaining power and reducing customers’ outside option.","PeriodicalId":433547,"journal":{"name":"Two-Party Negotiations eJournal","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130430226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Collaborators often invest unequal resources towards a common good. Without agreement on sharing that good, collaboration might devolve into parallel, possibly competitive, individual efforts. Reaching agreement requires bargaining. Before bargaining, collaborators independently decide how much to demand and how little to accept. These decisions constitute a tacit form of bargaining. When collaborators cannot verify a common construal of fairness, tacit agreement on equal shares offers the next-most obvious (least unfair) compromise between conflicting interests. Across two experiments, we show that reasoning to this conclusion requires more social-cognitive effort than people automatically expend. Participants played a card game with an alleged opponent and shared the resulting prize. Social-cognitive practice prior to tacit bargaining increased egalitarian proposals. Experiment 2 ruled out facilitation through general-cognitive effort or improvements in social-reasoning skills. Instead, we found that cognitive perspective-takers minimize unfairness, while affective perspective-takers seek minimal fairness. We discuss the differing implications of these motivations.
{"title":"Revisiting 'The [Social-Cognitive] Nature of Salience': Social-Cognitive Effort Focuses Attention on the 'Next-Most Obvious' Bargaining Compromise -- Equal Shares","authors":"John Voiklis, J. Nickerson","doi":"10.2139/ssrn.2136587","DOIUrl":"https://doi.org/10.2139/ssrn.2136587","url":null,"abstract":"Collaborators often invest unequal resources towards a common good. Without agreement on sharing that good, collaboration might devolve into parallel, possibly competitive, individual efforts. Reaching agreement requires bargaining. Before bargaining, collaborators independently decide how much to demand and how little to accept. These decisions constitute a tacit form of bargaining. When collaborators cannot verify a common construal of fairness, tacit agreement on equal shares offers the next-most obvious (least unfair) compromise between conflicting interests. Across two experiments, we show that reasoning to this conclusion requires more social-cognitive effort than people automatically expend. Participants played a card game with an alleged opponent and shared the resulting prize. Social-cognitive practice prior to tacit bargaining increased egalitarian proposals. Experiment 2 ruled out facilitation through general-cognitive effort or improvements in social-reasoning skills. Instead, we found that cognitive perspective-takers minimize unfairness, while affective perspective-takers seek minimal fairness. We discuss the differing implications of these motivations.","PeriodicalId":433547,"journal":{"name":"Two-Party Negotiations eJournal","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128242417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Acquirers and targets define and allocate interim risk through Material-Adverse-Event (MAE) exclusions in merger agreements. I examine why MAE-exclusions exist based on the risk they address and assess whether such risk allocation affects the gains in the acquisition. Targets and acquirers seem to use MAE-exclusions to signal target quality to reduce information asymmetry, and to allocate exogenous risk on the acquirer. I find little support for the use of MAE-exclusions to create commitment to alleviate moral hazard. Moreover, higher protection for the acquirer against information asymmetry on the target increases the value created by the acquisition. Overall, acquirers and targets use MAE-exclusions to preserve value in acquisitions.
{"title":"Risk Allocation in Acquisitions: The Uses and Value of MAE-Exclusions.","authors":"Antonio J. Macias","doi":"10.2139/ssrn.1392304","DOIUrl":"https://doi.org/10.2139/ssrn.1392304","url":null,"abstract":"Acquirers and targets define and allocate interim risk through Material-Adverse-Event (MAE) exclusions in merger agreements. I examine why MAE-exclusions exist based on the risk they address and assess whether such risk allocation affects the gains in the acquisition. Targets and acquirers seem to use MAE-exclusions to signal target quality to reduce information asymmetry, and to allocate exogenous risk on the acquirer. I find little support for the use of MAE-exclusions to create commitment to alleviate moral hazard. Moreover, higher protection for the acquirer against information asymmetry on the target increases the value created by the acquisition. Overall, acquirers and targets use MAE-exclusions to preserve value in acquisitions.","PeriodicalId":433547,"journal":{"name":"Two-Party Negotiations eJournal","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131508143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a variant of a general equilibrium model with group formation to study how changes of non-consumptive benefits from group formation impact on the well-being of group members. We identify a human relations paradox: Positive externalities increase, but none of the group members gains in equilibrium. Moreover, a member who experiences an increase of positive emotional benefits in a group may become worse off in equilibrium.
{"title":"A Human Relations Paradox","authors":"H. Gersbach, H. Haller","doi":"10.2139/ssrn.1823342","DOIUrl":"https://doi.org/10.2139/ssrn.1823342","url":null,"abstract":"We present a variant of a general equilibrium model with group formation to study how changes of non-consumptive benefits from group formation impact on the well-being of group members. We identify a human relations paradox: Positive externalities increase, but none of the group members gains in equilibrium. Moreover, a member who experiences an increase of positive emotional benefits in a group may become worse off in equilibrium.","PeriodicalId":433547,"journal":{"name":"Two-Party Negotiations eJournal","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128748232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a setting in which two potential merger partners each possess private information pertaining both to the profitability of the merged entity and to stand-alone profits, and investigate the extent to which this private information makes ex-post regret an unavoidable phenomenon in merger negotiations. To this end, we consider ex-post mechanisms, which use both players' reports to determine whether or not a merger will take place and what each player will earn in each case. When the outside option of at least one player is known, the efficient merger decision can be implemented by such a mechanism under plausible budget-balance requirements. When neither outside option is known, we show that the potential for regret-free implementation is much more limited, unless the budget balance condition is relaxed to permit money-burning in the case of false reports.
{"title":"Merger Negotiations and Ex-Post Regret","authors":"Dennis L. Gärtner, A. Schmutzler","doi":"10.2139/ssrn.1053461","DOIUrl":"https://doi.org/10.2139/ssrn.1053461","url":null,"abstract":"We consider a setting in which two potential merger partners each possess private information pertaining both to the profitability of the merged entity and to stand-alone profits, and investigate the extent to which this private information makes ex-post regret an unavoidable phenomenon in merger negotiations. To this end, we consider ex-post mechanisms, which use both players' reports to determine whether or not a merger will take place and what each player will earn in each case. When the outside option of at least one player is known, the efficient merger decision can be implemented by such a mechanism under plausible budget-balance requirements. When neither outside option is known, we show that the potential for regret-free implementation is much more limited, unless the budget balance condition is relaxed to permit money-burning in the case of false reports.","PeriodicalId":433547,"journal":{"name":"Two-Party Negotiations eJournal","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123732494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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