diff --git a/src/paper/references.bib b/src/paper/references.bib index 9b2bdd0..35796ae 100644 --- a/src/paper/references.bib +++ b/src/paper/references.bib @@ -884,7 +884,7 @@ @article{NavarroVeszteg2020 @article{NydeggerOwen1974, title = {Two-person bargaining: An experimental test of the Nash axioms}, author = {Nydegger, R.V. and Owen, G.}, - year = {1874}, + year = {1974}, pages = {239--249}, volume = {3}, journal = {International Journal of Game Theory}, diff --git a/src/presentation/defense.qmd b/src/presentation/defense.qmd index a98338b..4c6dea5 100644 --- a/src/presentation/defense.qmd +++ b/src/presentation/defense.qmd @@ -37,7 +37,7 @@ format: ::: ::: {.fragment} -- Many of such situations are characterized by an **imbalance of power** +- Many such situations are characterized by **power imbalance** - Employer vs. employees - Driver vs. passengers ::: @@ -70,7 +70,7 @@ format: ## This thesis ::: {.fragment} -- Focus on the case of +- Focus on - Predictions from **cooperative game theory** - **One** (few) **central player**(s) and many smaller ones ::: @@ -201,7 +201,7 @@ Same idea as with the Nash bargaining solution - Axiomatic reasoning - The Shapley-value is the only sharing rule that satisfies a **nice set of axioms**: efficiency, symmetry, linearity, dummy player axiom [@shapley1953additive] - **Bargaining foundations** - - The value arises as the subgame-perfect equilibrium of various alternating-offer bargaining games [e.g., @gul1989bargaining; @winter1994demand; @hart1996bargaining; @stole1996intra; @inderst2003bargaining] + - Subgame-perfect equilibrium of various alternating-offer bargaining games [e.g., @gul1989bargaining; @winter1994demand; @hart1996bargaining; @stole1996intra; @inderst2003bargaining] - A **tractable and sensible-looking** gain-sharing rule - Comparative statics show that it behaves as one would expect @@ -273,7 +273,7 @@ Set of all players: $N = \{P, A_1, \dots, A_n\}$ $$ v(S) = \begin{cases} 0 & \text{if } P \notin S \\ - f\left(\frac{\#_A (S)}{n}\right) & \text{otherwise}. + f\left(\frac{\#_A (S)}{n}\right) & \text{otherwise} \end{cases} $$ ::: @@ -290,14 +290,14 @@ $$ :::: {.columns} -::: {.column width="37%"} +::: {.column width="42%"} Characteristic fct.: $$ \scriptsize v(S) = \begin{cases} 0 & \text{if } P \notin S \\ - f\left(\frac{\#_A (S)}{n}\right) & \text{o/w}. + f\left(\frac{\#_A (S)}{n}\right) & \text{o/w} \end{cases} $$ @@ -305,7 +305,7 @@ $$ Shapley value: $$ \scriptsize -\varphi_P^n(f) = \frac{1}{n+1} \sum_{k=0}^{n} f(k) +\varphi_P^n(f) = \frac{1}{n+1} \sum_{k=0}^{n} f(k/n) $$ ::: ::: {.fragment .fade-in fragment-index=5} @@ -317,9 +317,6 @@ $$ ::: -::: {.column width=5%} -::: - ::: {.column width="58%"} ::: {.r-stack} @@ -356,14 +353,14 @@ $$ :::: {.columns} -::: {.column width="37%"} +::: {.column width="42%"} Characteristic fct.: $$ \scriptsize v(S) = \begin{cases} 0 & \text{if } P \notin S \\ - f\left(\frac{\#_A (S)}{n}\right) & \text{o/w}. + f\left(\frac{\#_A (S)}{n}\right) & \text{o/w} \end{cases} $$ @@ -371,7 +368,7 @@ $$ Random order value: $$ \scriptsize -\varphi_P^n(f) = \sum_{k=0}^{n} {\color{RoyalBlue}\Pr(|\mathrm{prec}P| = k)} f(k) +\varphi_P^n(f) = \sum_{k=0}^{n} {\color{RoyalBlue}\Pr(|\mathrm{prec}P| = k)} f(k/n) $$ ::: ::: {.fragment fragment-index=2} @@ -383,10 +380,10 @@ $$ ::: -::: {.column width=5%} +::: {.column width=4%} ::: -::: {.column width="58%"} +::: {.column width="52%"} ::: {.highlight-block .fragment fragment-index=2 .smaller} **Theorem 1.1.** @@ -765,9 +762,9 @@ Weighted value with **$\lambda_1 < \lambda_2$** ::: ::: {.fragment} -- Random order values are a **convenient tool** for modeling bargaining +- Random order values are a **convenient tool** for modeling bargaining in this setting - **Analytically tractable** - - More **flexible** than the Shapley value or the we + - More **flexible** than the Shapley value or the weighed value - **Sensible** in terms of comparative statics ::: @@ -782,7 +779,7 @@ Hybrid platforms and bargaining power ::: {.fragment} - Hybrid platforms are - Getting more and more common - - Seemingly obvious concerns and high-profile competition policy cases + - Apparent concerns and high-profile competition policy cases - Despite this, relatively little research ::: ::: {.fragment} @@ -799,7 +796,7 @@ Examine the bargaining power implications of hybrid platforms and their welfare ::: {.fragment} - **Shapley-value** based bargaining rule - - Analytically more **tractable** + - Analytically **tractable** - Has **bargaining microfoundations** [e.g., @hart1996bargaining; @stole1996intra] - Has precedents in the IO literature [e.g., @hart1990property; @montez2007downstream] ::: @@ -926,7 +923,7 @@ Utility function: @sec-utility-function ::: {.fragment} - Assume that the platform prices its products as if they were made by separate, competitive sellers - Possible interpretation: profit-maximizing subsidiaries - - More importantly: "best case scenario" + - More importantly: best-case scenario ::: ::: {.fragment .highlight-block .smaller} **Proposition 2.3.** @@ -1186,7 +1183,7 @@ Characterizing multiplayer free-form bargaining - Almost no structure - Group-level unrestricted **chat** - An interface for proposing and accepting allocations - - No binding decision until the very last second + - No binding decisions until the very last second ::: ::: {.fragment} @@ -1196,7 +1193,7 @@ Characterizing multiplayer free-form bargaining ::: {.fragment} - We test whether: - - Outcomes vary as we would expect, based on bargaining power + - Outcomes vary based on bargaining power as one would expect - Certain CGT solution concepts provide good predictions ::: @@ -1211,22 +1208,22 @@ Characterizing multiplayer free-form bargaining :::: {.smaller} ::: {.fragment} - Early unstructured bargaining papers (1950s-1990s): - - e.g., @Kalischetal1952, @Maschler1965, @NydeggerOwen1974, @RapoportKahan1976, **@MurnighanRoth1977**, @MurnighanRoth1978, @Micheneretal1979, @MichenerPotter1981, **@LeopoldWildburger1992** + - @Kalischetal1952, @Maschler1965, @RapoportKahan1976, **@MurnighanRoth1977**, @MurnighanRoth1978, @MichenerPotter1981, **@LeopoldWildburger1992** - Face-to-face bargaining, different experimental standards ::: ::: {.fragment} - Free-form bargaining - - e.g., @Galeottietal2018, @HossainLyonsSiow2020, **@NavarroVeszteg2020** + - @Galeottietal2018, @HossainLyonsSiow2020, **@NavarroVeszteg2020** - Almost always bilateral ::: ::: {.fragment} - Multi-lateral bargaining - - e.g., @MonteroSeftonZhang2008, @MitsutsuneTakanori2014, @TremewanVanberg2016, @chessa2023experiment, **@ShinodaFunaki2022** + - @MonteroSeftonZhang2008, @MitsutsuneTakanori2014, @TremewanVanberg2016, **@ShinodaFunaki2022**, @chessa2023experiment - Structured or semi-structured ::: ::: {.fragment} - Fairness views in bargaining - - e.g., @LuhanPoulsenRoos2019, @Schwaninger2022, **@ClippelRozen2022** + - @LuhanPoulsenRoos2019, @Schwaninger2022, **@ClippelRozen2022** ::: :::: @@ -1328,12 +1325,16 @@ How to divide the value between the players? - Even in the dummy player treatment! - $Y=10$ and $Y=30$ treatments still look similar - In the $Y=90$ treatment - - $A$ only achieves significantly higher by excluding one small player (@sec-timing) + - $A$ only achieves significantly higher payoff by excluding one small player - Neither efficient nor stable ::: :::: +::: {.crossref} +Timing of agreements: @sec-timing +::: + ## Testing the axioms {#sec-axioms} @@ -1384,13 +1385,15 @@ Details: @sec-axioms-appendix ::: {.crossref} All chat messages: @sec-chat-topics-all + +Example chat messages: @sec-chat-example-stability ::: ## Main takeaways ::: {.fragment} -- Lots of **equal splits** in all treatments, but considerable **heterogeneity** +- Lots of **equal splits** in all treatments, but considerable **heterogeneity** between participants - Heterogeneity in fairness concepts? - Norms established in early rounds? ::: @@ -1399,7 +1402,7 @@ All chat messages: @sec-chat-topics-all - No bargaining power advantage when there is no profitable deviation ::: ::: {.fragment} -- Both **overestimate big player's share** +- Both **overestimate the big player's share** - They do not capture all relevant fairness considerations - Combining other-regarding preferences and CGT might be promising ::: @@ -1670,7 +1673,6 @@ $$ ## Utility function {visibility="uncounted" #sec-utility-function} -::: {.incremental} - Follow @anderson2021hybrid - Unit mass of customers, each choosing one product maximizing $$u_{ij}^T = v^T - p_i^T + \mu \varepsilon_{ij}^T$$ - $T \in \{P, F, 0\}$ @@ -1678,7 +1680,6 @@ $$ - $v_T$: value of the product - $\mu$: degree of horizontal differentiation - $\varepsilon_{ij}^T \sim \mathrm{Gumbel}(0, 1)$: taste shocks -::: ::: {.crossref} 🔙 @sec-demand @@ -1864,26 +1865,36 @@ $$ ::: -## Chat – Stability-based reasoning {visibility="uncounted"} +## Chat – Stability-based reasoning {visibility="uncounted" #sec-chat-example-stability} ::: {layout-ncol=3} -![Y = 10](/out/figures/chat_excerpt-2702-2707.svg){.chatlog} +![Y = 90](/out/figures/chat_excerpt-6846-6847,6849,6851,6853,6855,6857,6859.svg){.chatlog} ![Y = 30](/out/figures/chat_excerpt-5640,5647-5648,5660-5663.svg){.chatlog} -![Y = 90](/out/figures/chat_excerpt-6846-6847,6849,6851,6853,6855,6857,6859.svg){.chatlog} +![Y = 10](/out/figures/chat_excerpt-2702-2707.svg){.chatlog} +::: + +::: {.crossref} +🔙 @sec-chat-topics ::: + ## Chat – Fairness-based reasoning {visibility="uncounted"} ::: {layout-ncol=3} +![Rejecting small offers](/out/figures/chat_excerpt-7894-7901,7906.svg){.chatlog} + ![Equal split](/out/figures/chat_excerpt-7052,7054,7057-7063.svg){.chatlog} ![A gets a bit more](/out/figures/chat_excerpt-7590-7596,7598-7599.svg){.chatlog} +::: -![Rejecting small offers](/out/figures/chat_excerpt-7894-7901,7906.svg){.chatlog} +::: {.crossref} +🔙 @sec-chat-topics ::: + ## Chat – Dummy player treatment {visibility="uncounted"} ::: {layout-ncol=3} @@ -1894,14 +1905,23 @@ $$ ![Appeal to pity](/out/figures/chat_excerpt-1371-1376.svg){.chatlog} ::: +::: {.crossref} +🔙 @sec-chat-topics +::: + + ## Chat – Feedback about experiment {visibility="uncounted"} ::: {layout-ncol=3} ![Having a chat](/out/figures/chat_excerpt-6508-6509,6511,6513,6524,6527,6528-6529.svg){.chatlog} +![Bargaining time](/out/figures/chat_excerpt-5501-5508.svg){.chatlog} + ![Payouts](/out/figures/chat_excerpt-286-291.svg){.chatlog} +::: -![Bargaining time](/out/figures/chat_excerpt-5501-5508.svg){.chatlog} +::: {.crossref} +🔙 @sec-chat-topics :::