Dear Karolina, can you please specify what you have in mind according to employee bargaining power? Coverage by collective agreements or the increase of collectively agrees wages or,,,?

to follow up on Claudia, this needs specification. in my research, I've for instance separated between direct-representative; individual-collective and formal-informal creating a range of alternative forms including formal union negotiations, individual assessment interviews, haggling, workplace meetings, etc. And that is just the forms, then you have to think about the level of influence (or bargaining power if you will) of the different forms - which is not a zero sum game.

There are numerous studies, although they may not give you directly what you are looking for. Examples:

Philip Manow: Comparing Welfare Capitalism (2001), Chapter 2: Business Coordination, Wage Bargaining, and the Welfare State

Taekjin Shin: Explaining Pay Disparities Between Top Executives and Nonexecutive Employees - a Relative Bargaining Power Approach, Social Forces June 2014, pp. 1339-1372

Ricky Siu Wong: Knowledge of Opponents' Power in Power-Asymmetric Negotiations: Whose Knowledge Shapes the Structure of Outcomes? in Contemporary Management Research, June 2015, pp. 117-142

Aaron Pacitti: Bargaining Power, Labor Market Institutions, and the Great Moderation, Eastern Economic Journal, Spring 2015, pp. 160-182

Samantha Farmakis-Gamboni & David Prentice: When Does Reducing Union Bargaining Power Increase Productivity? Economic Record 2011, pp. 603-616

Michael Leroy: The Power to Create or Obstruct Employee Voice: Does US Public Policy Skew Employer Preference for "No Voice" Workplaces? Socio-Economic Review 2006, pp. 311-319

Krishna Chaitanya Vadlamannati: Rewards of (Dis)Integration: Economic, Social, and Political Globalization and Freedom of Association and Collective Barganing Rights of Workers in Developing Countries, Industrial & Labor Relations Review 2015, pp. 3-27

There are hundreds more publications along these lines but I would also need to know which specific questions you are researching...

You might find some of the following points helpful.

Establishment level union density may proxy union power but whether that power is wielded in the direction of destructive or constructive ends will depend on management's response to the union

https://www.researchgate.net/publication/259547469_Are_Unions_Good_or_Bad_for_Organizations_The_Moderating_Role_of_Management%27s_Response

or its co-existence wtih individual voice mechanisms

https://www.researchgate.net/publication/279033571_Balancing_efficiency_equity_and_voice_The_impact_of_unions_and_high-involvement_work_practices_on_work_outcomes

On the differences between direct/individual and representative/collective voice see

https://www.researchgate.net/publication/4736991_What_Kind_of_Voice_Do_Loyal_Employees_Use

Best wishes with your work, Andrew

Article Are Unions Good or Bad for Organizations? The Moderating Rol...

Article Balancing Efficiency, Equity, and Voice: The Impact of Union...

Article What Kind of Voice Do Loyal Employees Use?

This article may be useful:

Hausken, K. (1997), “Game-theoretic and Behavioral Negotiation Theory,” Group Decision and Negotiation 6, 6, 509-527.

Article Game-theoretic and Behavioral Negotiation Theory

There is a wide range of articles about your theme. My suggestion is that you can specify your topic and then search for previous published papers.